1) In addition to the Avenues and Sugar House (I'd lean more toward the Avenues if you'll be working near the University), downtown neighborhoods would be a great option for you. 9th & 9th and Liberty Park neighborhoods would be good places for single 20-somethings. The Marmalade/West Capitol Hill neighborhood is rife with single young people, and it's a very fun residential area, close to events downtown. It's probably my current favorite neighborhood for those without families.
All five of these areas, however, have more single-family homes, with a few multi-family.
2) For a larger apartment complex---particularly what would pass as a "high-rise" out here, you'll have to look more downtown, almost in the central business district (which does have plenty of apartments). My favorites are American Towers on 300 South and Main, Broadway Lofts, Westgate Lofts, Dakota Lofts. There are dozens of apartment buildings along the eastern portions of 300 South, 200 South, 100 South, etc. I doubt you'll end up sharing an apartment here; most young people living with roommates are doing so in big, old houses and that type of thing. Apartments seem to be more solitary, as they're quite affordable, compared to other large-ish cities. The Gateway district (not just the Gateway itself) is also a neighborhood to consider. I also love Central City; it has a mix of older homes and apartment complexes; it's very young and is well-located, and among the most affordable areas. (I live there, if you couldn't tell!)
American Towers has a pool and gym on-site, though I'm not sure what availability is like. The Gateway has an on-site gym, but no pool. Apartmentguide.com can also suggest complexes that have pools. Some places that friends have liked: Palladio (central business district), Jefferson School (Central City), Irving Schoolhouse (Sugar House), Park Capitol (Marmalade).
An easy way to decide if a place on ApartmentGuide is in the location you want is ZIP code. You'll want to stay in 84101 (downtown), 84111 (downtown), 84102 (Central City/University), 84103 (Avenues/Marmalade), 84105 (Sugar House). Everything else is further outside of downtown (84104, 84106) or more family-oriented (84108, 84109).
3) MeetUp.com is a great suggestion---the MeetUp culture has become quite active in SLC. I don't ski, but my friends who do always go together in groups. That's not to say singles aren't out there, as many people skiing in the middle of the week are on the slopes alone because they alone have a day off work. Meeting people at coffee shops and live music venues is also a good option, as well as hiking clubs, skiing clubs, team sports, even some purely social clubs like
Drinking Liberally of Salt Lake City (though that one's definitely not for the politically conservative!).
4) SLC has a host of wi-fi spots around town. There are a few dozen coffee shops, bookstore, cafes with wi-fi; and large portions of the downtown area have public wi-fi (Main Street, Library, Liberty Park) provided by X-Mission. I think you'll find SLC to be among the most computer friendly cities around. Thanks to the University of Utah being a founder of the Internet from the 1960s onward, we're a pretty well-wired city. UTA light rail and commuter rail feature free wi-fi, and the commuter rail has charging stations, too. My favorite cafe/coffee shops with wi-fi: Coffee Garden, Nobrow, Les Madeleines, Sam Weller (soon to relocate, however), Beans & Brews, Salt Lake Roasting Company, Salt Lake Coffee Break.
5) Depends on what you're into. There are surprisingly good local music venues; Salt Lake has an acknowledged underground music scene that rivals much bigger cities'. The Urban Lounge, Kilby Court, In the Venue, all host up-and-coming acts. There are some great museums, unexpectedly cosmopolitan restaurants, and a host of fun brewpubs and bars. As you said, this won't be NYC nightlife, but you can have a very busy night out.
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Relocation to SLC - Single, 20s - Questions
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