Playing music is a lot like drinking whisky.
Either it’s a social thing you do with friends, or you become a pro and do it by yourself all day. 
Seriously - amateur musicians need other amateur musicians to play with. It’s far more important than your choice of instrument.
My mom plays and uses sites like this: Ukulele Chord Chart - Standard G C E A Tuning - Ukulele Songs, Ukulele Tabs, Ukulele Chords, Ukulele Lyrics, Ukulele Tuning
And Youtube where someone shows how to play a popular song on Uke: https://m.youtube.com/watch?v=cOeJ7EOUIyQ
Lots of good advice here. Just came in to say that my aunt had a similar childhood experience to the OP, but had musical daughters and nephews and always regretted not being able to play music. For her 50th birthday she bought herself a clarinet and set herself on learning it. Within months she could play a tune and after a couple of years, joined a local amateur orchestra which she then enjoyed very much for the rest of her life. So I’d say absolutely go for it - you’re never too old, with a bit of time and determination you can do something that will give you and others a lot of pleasure.
Thanks for the advice. I had also thought about getting a keyboard.
Are there electronic keyboards which can produce arbitrary/programmable sounds? By which I mean: If you’re using electronics to turn motor inputs into sound outputs, then the sound outputs have the possibility of being whatever you want. You could have an electronic keyboard which outputs flute, guitar or trumpet sounds. Is this accurate? If so, how does the quality of that sound tend to be? Is it late 90s Geocities blog MIDI-like?
There are tons of books and sites with uke music and tablature, just look on amazon or websites already mentioned. I like Rob MacKillop’s books but every player has their favorites of course.
For me, the quickest way to learn an instrument was to be inspired to the point of desperation. When I started fingerstyle guitar, I just HAD to play this or that song. Some songs are within reach when starting out, some are further away but can be gotten to with perseverance. The hazard with this is having instruments that don’t get played enough but I can accept that.
I always found having some sort of keyboard to be handy even if just for figuring stuff out. I even resorted to using a GarageBand keyboard on my iPad recently.
Electronic keyboards these days can produce the sound of just about any instrument, and quite nicely, but the hard part is getting it to sound like the instrument is actually being played. Do you have a music store nearby? A decent salesperson could walk you through the different options.
Hell - try playing upright bass! $175 would be a bargain! :smack:
I second (third? fourth?) the recommendation for uke. There is tons of music available, either in stores or on-line. There also are a ton of uke Meetup groups, if you are in any largish city. Great way to get better faster.
Realize there are several sizes of uke. And banjo ukes - which give a neat (IMO) sound. I suggest the baritone uke, which is tuned differently than the others - same as the top 4 strings of a guitar. Chords and melody patterns would switch readily should you wish to change to guitar. But the nylon strings are easy on the fingers, and more widely spaced. There are some on-line communities (Humble baritonics is one IIRC.)
Tenor guitar is another option which is different than a standard guitar. Especially lends itself if you like certain types of music. There is often an overlap between bari and tenor guitar players.
With uke, there is a TON of material on Youtube - not only tutorials, but also more advanced stuff, to see if that is something you might aspire to.
I think I paid around $180 for my bari. Bought my grandkid a soprano uke for around $40 - which is definitely playable (and bright red! ;)).
I also agree with the harmonica suggestion. I’ve long believed that there is no instrument that is more portable yet more flexible. Put a harp in your back pocket and you can make music walking down the street, waiting for a bus, on a business trip, etc. Good harp will cost you around $30. Only downside is you’ll eventually have to buy at least a couple in different keys.
If you choose banjo, you have to decide between bluegrass and clawhammer style. I prefer clawhammer, if for no reason other than that you don’t need to mess with picks. I found BG style very hard. Have long meant to learn clawhammer. The banjo player in my group always tells me how easy it is, but I never take the time to work on it, realizing how much work I need to put into playing bass.
Speaking of what NOT to pick up - don’t play upright bass. I mean, it is a cool instrument. And I tried many other instruments before realizing that I was a bassist. But it is absolutely ridiculous to haul around.
Absolutely agree with this.
Dulcimer is a diatonic instrument; that means there are no wrong notes.
You don’t have to learn to read music; there are tons of TABs around for dulcimer.
You will be playing your first song in a matter of minutes.
If you play in noter and drone style there is none of the intense fingertip pain associated with learning guitar. A noter is simply a wooden dowel you use to press the string (you only press one string on a dulcimer [technically, that one string is actually two strings but the are always played together as one string]). Search on youtube for ‘dulcimer noter drone’ for examples.
About 10 years ago I bought a cheap electric guitar and attempted to learn to play it. Things didn’t go well so I got rid of it. A few years ago I got to try an Ibanez guitar. It was so much easier to play than the cheap guitar I bought it and tried to learn to play it. Last year I bought a 4 string cigar box guitar. Even easier to play. I have become okay on it, apparently good enough I got a chance to jam with a buddy’s band and was good enough to be invited to play with them again. I recently removed 2 of the strings off the Ibanez and have using what I learned on the cigar box guitar. It’s a work in progress but I’m not giving up this time. I’m retiring from my job in a few months and I plan on spending a few hours a day minimum practicing.
I used to play the harp while waiting for the bus, but once I boarded, the driver would tell me to shut up.
This is what I suggest. A baritone will make a transition to guitar easier if you decide you like it and want to add a couples strings. I have a tenor and baritone uke but I rarely touch the tenor since I mainly play guitar or bass.
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I’ve always loved the sound of the cello. So, on the day I turned 70, I began teaching myself to play. 2-1/2 years later, I can play reasonably well, though I’ll never be a virtuoso. I play for my own pleasure, not for an audience, and I’m happy staying that way. If I had settled for an easier instrument, yeah, I may be playing better by now, but I may not get as much pleasure from it.
Fine - you keep it tuned. 
No big deal, especially compared to my tiple.
All my life I’ve had one guitar or another lying around but never got very good at playing them. Never stuck with it. A year ago I went out and picked up a pretty good electric and have been off and on downloading basic lessons and songs. In comparison to the old days when I tried to teach myself out of books purchased at the music store, You-Tube is an absolute wonder. If you want to learn the basics there are lots and lots of options in different styles from beginner to advanced, and if you want to learn a particular song you can usually find a demonstration video, assuming the song isn’t too obscure.
The advantage to the electric guitar is that you can play it with the amp turned down so that neighbors/housemates don’t have to hear you torturing it. You might appreciate that given that you live in an apartment. I assume you can do the same with an electric keyboard.
Kill me now the way I play is not conducive to tuning stability. Those three-string courses would sound awful and clashy in my hands.
I’m left-handed and doubt I’ll have much skill playing with my right hand. How much would that matter for an acoustic guitar?
I suppose it’s possible to plug it into a computer then listen through headphones, correct?
What are your goals?
What type of music do you want to play? Do you want to learn just enough to sing your favorite songs? Learn enough to play your favorite songs without accompaniment? Do you care at all about portability? Do you want to join a band that plays at open mics and maybe even paying gigs? Join a band that’s really just an excuse to drink on the weekends in somebody’s living room? Never ever play in public at all?
That’s not to say you can’t do these things with just about any instrument, but if your goals are very modest then you should spend a very modest amount of money on a very modest instrument. Better to spend fifty bucks on a cheap uke and then decide to upgrade later than to spend two hundred bucks on a cheap guitar and realize you’re not having fun.
It’s out there, but you do have to do a little digging - especially if you’re looking for a specific song. Best practice for uke music is to kind of just kind of trawl the internet for anything that looks cool. I like ukulelehunt.com.
I would love to learn to play the trumpet.
Many guitar amps have a headphone jack, as well.