Most of what I would recommend has already been touched on - Lagavulin for a strong scotch, and Balvenie Doublewood as a good solid middle of the road drink.
I did’t see Ardbeg mentioned - this one’s another good, peaty scotch.
Jonny Walker Green got me started on scotch - it’s blended with a little of the peaty stuff, but it’s got more going on than just the smoke.
You should be able to pick up a Glenlivet 18 yr old for around $110, more or less.
So yeah, something in the low-mid $100’s would be, as recommended above;
Highland Park 18
Talisker 18
Bowmore 18
Glenlivet 18
Good ‘fancy’ and older scotch, make you feel good to have something like that on hand.
All I can add to this thread is ‘me too’.
Another avenue is to head off to your local liquor warehouse (does Pennsylvania have such things?) and explore the independent bottlings of Murray McDavid or Gordon & McPhail. Great stuff to be found there. I tripped over a 20 year old bottling of The Glenlivit a few years back that was transforming.
Don’t rule out anything by Bruichladdich (I greatly enjoyed the 15) or Auchentoshan (the Three Wood is very drinkable and affordable, relatively speaking). Just so you know where I’m coming from my usual tipples are The Macallen and/or Glenmorangie or Glenfarclas 12-15s. A’bunadh is amazing but not like anything else I’ve ever tried.
For an experience I’d suggest Springbank 15 year old. Clean and peaty without being peaty tasting…liquid peat?
Now, about 20 years ago I had a chance to play in a bonspiel sponsored by Glenfarclas (or drinks provided or something). The environment was perfect for it and it was sweet without being cloying and warming without feeling like you licked a charred stick. Might be worth it to try a 12 year old, assuming no one’s had a more recent experience.
Assuming silenus has your budget right maybe look to pick up 2 bottles of 10-15 year old scotch instead of a single 15-20 year old bottle.
With Scotch, peaty and smoky are really the same thing - or at least aspects of the same thing. They don’t actually shovel peat moss into the whisky, though with the way a few examples taste you wouldn’t be blamed for thinking so. 
At one point in the process, the malt has to be dried. Whisky-making being as old a process as it is, the generally-accepted method of getting it dry is to heat it over a fire. Irish whiskey’s malt is dried over a peat fire, as Scotch is, but in the Irish tradition, the malt that’s being dried is in a container that protects it from the smoke. The Scots tend to heat theirs a little more directly, so theirs does get exposed to some smoke. (Some more than others, as you’ve noticed.) Exactly what that smoke tastes like in the finished product depends on how dry the peat was, who built the fire, what the ventilation is like there, and whatever other variables.
Why do the Scots and the Irish use barley malt dried over a peat fire, and not corn or rye dried over a wood fire? Why do the Americans favour corn? And why do the Poles make some of their vodka from potatoes? Answer in all cases: Because they knew where to get a lot of it, cheap.
Exactly. You can talk about national character and style and all that malarky all you want, but the national booze will be made of whatever was abundant and cheap.
Ardbeg’s 2018 Feis Ile Committee Release, “Grooves”, is just hitting the states, and I think it’s amazing. The Committee Releases are all usually great; I found this year’s locally for about $110, though other places have it higher. Worth grabbing if you find it.
Talisker Distiller’s Edition can usually be found for around $100, and that’s the bottle I usually end up reaching for when I want to “kick it up a notch.”
Balvenie’s 12 year old First Fill Single Cask, again about $100, is different for a Balvenie - it hasn’t had the sherry cask finish. Their Doublewood uses second-fill and later, so new barrels are “worked in” with the first fill. This is a marvelously smooth whisky; you can still taste the Balvenie character, but the first-fill barrels give it a very distinct flavor.
Anyway, that’s a couple that are a little off the beaten path.
Slainte!
My FIL bought that one. It was wonderful.
How does Grooves compare to other Committee offerings, like “Day” or “Alligator?” I was going to recommend one of the Committee ones to NAF1138, given he mentioned he liked Laphroaig, as they’re very distinctive, but usually still have that Islay brine and peat. (Alligator is a bit of an exception, being one of the most Bourbon-y Scotches I’ve ever tried.) Ardbog (the spelling is intentional) is also awesome, and one of the best Scotches I’ve ever had.
NAF, I’ve found that the older you go, the more they all tend to converge on treacley, smokey, warming goodness, but lose a lot of the individual regional character that made you pick up an Islay instead of a Lowlands. If you want a beautiful, Bourbon-y, brandy-like Scotch, it’s hard to beat something like a Glenfarclas 21 year. If you like the Sherry-heavy taste, OTOH, nobody does that better than Macallan.
You mentioned you tried Lagavullin; what did you think? IMHO, I haven’t liked them as much since their fire. Never mind the massive price increase.
EDIT: Liking Laphroiag makes this quest a bit easier, as liking it means that there pretty much isn’t a Scotch that you’re going to find to be too much like iodine and smoke. If you’re feeling really spendy, some of the Port Ellen older bottlings are supposed to be very good. As silenus noted upthread, Bowmore is also an excellent choice. I’m not as big a fan as some for the crazier peated ones from Bruichladdich, but they’re certainly spendy and filled with phenol. What is Octomore now anyway? Something like 150 ppm phenol?
But don’t say the name out loud… it’s a Hogwarts spell.
Y’know, this is where my “try before you buy” method breaks down… when you can’t find a bar that serves a particular scotch you’ve heard of.
Anyone want to invent an app? I’d love one that lets you type in a spirit (or beer or wine) and it’ll show you places that serve it, or even make drinks featuring it.
(Just as we were discussing scotches here, I saw a drink made with “Monkey Shoulder, vermouth and orange”) … the Blood & Sand at the Robin Room.
(a separate screen could tell you the closest place to buy it and the price… oh, wait, that’s called Google)
You can make it cheaper using pork shoulder, but it’s just not the same somehow. 
Ok, since there have been several great responses to this thread and since most of the um, er, experienced drinkers (looking at you, silenus) are here, and I don’t really want to resurrect an older thread about whiskey, I’ll just mention this here. Jim Beam Double Oak bourbon. $18 at my local Walgreens. Wow. This stuff punches well above it’s price. If you see this on the shelf, snap it up. Well worth a try.
For single malt.
Sometimes, older is better. Often, in fact. Not necessarily always, though - it depends what you like. Especially when you get to the oldest available, there are certainly people who say that excessive aging eventually leads to something that’s less interesting and has less character than the slightly younger version.
Plus the fact that any truly good whisky at 10 years is already better than mediocre whisky will ever be. Magic doesn’t happen.
Gray Ghost:
Of the Feis Ile releases I’ve tried, this one rates - for me, anyway - probably second best, but a distant second from the amazing Auriverdes. Grooves has a much smoother and more pronounced mouth-feel; you get a nice, smoky smoothness, lots of spices but not an overwhelming “oiliness” (I think the Alligator was a bit too salty/oily, but it’s been a long time since I’ve had it). The finish is cinnamon; I was reminded of how your mouth feels after eating a Red Hot candy.
NAF, age isn’t everything; a well-aged whisky in crap barrels is likely to be a an old crap whisky (thankfully, few and far between). For instance, I much prefer the Balvenie 17 year Doublewood to their famed 21 year Portwood, and the difference is, of course, the finish barrels. I also prefer the Aberlour 12 over the 18, as Aberlour is kind of a light, sherry-finished whisky, and the 18 is just kind of flat as far as character goes.
And don’t necessarily overlook the NAS (No Age Statement) offerings. Some are just attempts to extend existing but diminishing stocks by blending, but a great many are very well-crafted. As I mentioned above, the Ardbeg Auriverdes and Grooves are fine examples.
It’s all individual taste. As an old acquaintance once told me, “Any whisky you’re enjoying is a good whisky.”
And this is where it gets overwhelming quickly. I am going to have to track down some of those bars **silenus **linked to and sample some stuff. Anyone wants to come to Philly I would be happy to sample stuff with you guys.
That said, I have a small list of things to look for at the local state store. I am leaning toward something from Talisker based on this thread, only partially because I am pretty sure I have seen it on the shelf in the past and it sounds like I probably can’t go wrong with whatever they have on the shelf. I think I have also seen Balvenie Double Wood. If I see Ardbeg I may give that a shot, what is available when I go shopping will make my final decision. Those three are all names I recognize from staring at the scotch shelf before I started this thread, so I think they should have one of them (I know they have something from Talisker, maybe only the 10). Though if anyone thinks something is VERY worth a special order let me know. I can get almost anything I want, but it takes a week to show up if I special order.