It is as much a thing of personal taste as wine. Well, maybe not as much. I am perfectly happy with Bushmills and water.
I’m surprised nobody has mentioned Blackadder yet. That stuff is liquid gold. I love their Islay scotch when I can get it.
If you want even more smoke, Clear Creek Distillery’s McCarthy’s Oregon Whiskey is like Ardbeg used to be.
If it’s peat, and not just peat smoke you’re looking for see if you can find a Springbank.
Alas. 
Guess I’ll nurse the last half of the bottle I bought a decade or so ago…
For people who don’t like whisky because they prefer something smoother/sweeter, I’ve found the Glenfiddich Malt Liqueur to be a nice compromise - still has a good whisky taste, but sweeter and syrupy (I find it a bit more “whisky-tasting” than Drambuie or Irish Mist)
FWIW, I went on what I assume is the same whisky tour msmith537 mentioned in Edinburgh (the scotch whisky experience, just near the castle), and would definitely recommend it.
I tried some of the Bowmore there and really liked it, and found it quite smooth to drink (my mum found that one pretty easy to drink as well, and had the same problem as you with most of the others)
On a side note, how is “Lagavulin” pronounced?
I’ve been hearing “luh-GAH-vuh-lin” in my head; is that even close? I don’t wan’t to sound like an idiot if I decide to try some next time I’m out…
It starts with lah (as in laparoscopy), nut luh.
http://www.thewhiskystore.de/dist/lagavuli/lagavuli.wav
If you’re looking for a Scotch with lots of smoke and peat and all-around character, but you’re on a budget, Teacher’s Highland Cream is definitely the way to go. It’s a blended Scotch, but it’s got more malt in the blend than other blended whiskies, and it’s quite reasonably priced. About the same as a bottle of Dewar’s.
Oooh - I’ll have to try that. I really can’t deal with Laphroaig’s massive peatiness (it’s like licking Scotland!), but I think I could deal with a blended.
For anyone looking in this thread for a scotch recommendation that doesn’t taste like band-aids, I’ll recommend Balvenie DoubleWood, a wonderfully smooth single malt.
As with most whisky names it’s an anglified spelling of a Gaelic name. Lowlanders in Scotland generally pronounce it with the stress on the 3rd syllable (‘voo’), but that’s no indication of how the unanglified name would be pronounced by Gaelic speakers on Islay.
By the way, most people pronounce ‘Glenmorangie’ with the stress on the 3rd syllable, but locally (an area where Gaelic is no longer spoken) the stress is on the 2nd.
For homework, get your tongue around ‘Bunnahabhain’, which is one of the few that uses a Gaelic spelling. "Bh’ is pronounced ‘v’ and I think the first ‘h’ is silent.
If you’re interested, ‘Garioch’ is a Lowland placename which is pronounced ‘Geeree’ (with a hard ‘g’).
Check out this pronunciation guide.