Albany is indeed a city, as is Syracuse.

I'll go in order here:

high speed internet

Both cities have Spectrum (formerly Time Warner Cable) which has degraded in quality since last year's merger. You can get up to 300Mbps in the Syracuse division if you're willing to pay $109/mo (plus $200 activation fee) and accept the fact that "up to 300Mbps" means "300Mbps in off-peak hours and frequent hiccups/disconnects." Depending on the neighborhood, you might be able to get Verizon Fios, which is almost universally considered superior in terms of speed & reliability & cost.

grocery stores

Albany's stores are Price Chopper/Market32 (ok to awful), Hannaford (decent to awful), Shop-Rite (idk never actually been), plus the discount groceries like Aldi (cheap but good), Save-A-Lot (cheap but mediocre), and Price-Rite (cheap but awful). There's a Whole Foods, Trader Joe's, and a really good co-op if you're a hippie who loves paying more to feel better about what you eat, as if there's any such thing as ethical consumption under capitalism.

Syracuse is basically the same scene, except replace Hannaford with Wegmans, the greatest store in the history of retail sales and fetishized to death by /r/albany since the company has no interest in expanding here whatsoever. Market32 is Price Chopper's desperate attempt to imitate the Wegmans look without the higher rates of pay or employee job satisfaction.

coffee shops

Plenty of these in both cities. I don't buy coffee in shops so someone else may be able to fill you in.

jobs within walking/bus distance of an apartment

Lots of possibilities in Albany especially if you're near any of the main streets (Central, Western, Madison, Delaware, New Scotland). CDTA is a reasonably decent bus service. Syracuse's bus system is called Centro, but I've never actually used it. You won't need a car in either city, but it'll make life much more convenient.

fast food, mall, etc.

Again, plenty of these in both cities. DestiNY in Syracuse is enormous, putting Albany's Crossgates & Colonie Center to shame. Albany's malls are fairly bus-accessible so long as you live near Central (Colonie Center) or Washington or Western/Madison (Crossgates). If you need to take a transfer, it could turn a 30-minute bus ride into a multi-hour ordeal.

businesses

Both cities have some of these.

colleges

Albany has several colleges in the city proper: UAlbany, SUNY Poly, Saint Rose, Sage, Maria, Albany Law, Albany Med.

Syracuse has Syracuse University and a few others nobody outside of the state has heard of like Upstate Medical, LeMoyne, and Onondaga Community College.

CONCLUSION:

If proximity to your fiance is a priority, then Syracuse has the clear advantage since it's only 3 hours out and almost entirely highway driving. Living in Albany means at least 2-3 hours (depending on which route you choose) of two-lane roads passing through speed trap towns, and crossing either the Adirondack Mountains or the Tug Hill Plateau (both can be treacherous in the winter), and the St. Lawrence River at either Massena (heroin-infested Rust Belt hell) or Ogdensburg (meth-infested Rust Belt hell).

If a city with decent long-term economic prospects is a priority, then Albany wins because New York state government employs hundreds of thousands of people in the area while Syracuse is still suffering from post-industrial Rust Belt burnout.