First, welcome to town. I love Denver because it is a real city, at the same time that it doesn't get all impersonal like some of the other major cities in the country. This is the kind of town where it is normal to strike up a conversation with a stranger on the street. The best thing about this town is that it has a lot of funk and there are people from all walks of life here.
First, I would not live in the Cherry Creek area. It is the most affluent part of town, and by correlation, the least diverse and the most snooty. Yeah there are nice places to shop there, and that's about the only reason I go to Cherry Creek.
A lot of guys will be giving you advice about our gayborhoods in and around Capitol Hill, so I'll skip those. Capitol Hill is a fun place to live, but it can be very much of a 24/7 neighborhood- lots of noise and crazy activity at all hours of the day.
Light rail: Someone mentioned here that if you're in interior Denver, you won't need it. That is true: you're so close to downtown that you should either be walking or taking a local bus. If you're in Capitol Hill, you could walk to Metro State in under 30 minutes. The RTD bus system here is great and I use it all the time, although the 15 in particular tends to get a little crowded and seedy. All other routes are just fine and very efficient. The best thing to do to get to Metro is to take a bus downtown, and transfer onto the light rail for just one stop, which will drop you right off on the main campus. Look at an RTD system map if this helps you decide on what areas are best for your transit needs: www.rtd-denver.com
Neighborhoods in Denver proper are very inner city, and change in name and character about once every six to ten blocks. The city starts to spread out quickly though, and by the time you get close to Colorado Boulevard, you can easily find great houses with nice yards. The closer you get to downtown, the less yard space you have, until ultimately you're in condo and apartment situations.
For six years I used to live down in the 1st Avenue and Grant area. That was a great neighborhood. A lot like Capitol Hill, but quieter at night. I could get downtown in 10-15 minutes on the bus (the 0.) It's getting to be a trendy area of town and rents there are going up, but are still reasonable.
I love the areas along either side of Alameda, between Broadway and Downing St. If you lived in this area, you could take the 3 west to the lightrail, transfer, and then be at Metro in about 30 minutes.
West Washington Park is an AWESOME area and pretty affordable. It is generally south of Alameda, and between Broadway, Downing, and I-25. But the bus lines aren't the fastest to get from here to downtown. Rents are reasonable, but not cheap.
Congress Park is a lot of fun. It is basically the next neighborhood out from Capitol Hill. It is still very much inner city, but just a hair more room for houses and apartments. Easy bus transportation to get from here to downtown. This neighborhood has a great housing stock. You can still rent an economical shoebox in this neighborhood if you need to, but there are some super nice homes too.
If you can relax a bit and aren't too worried about living near a gay epicenter, lol, check out some of the neighborhoods east of Colorado Blvd, between Glendale and 17th Ave. There are some nice places here, still city, but 1940s neighborhoods that are just starting to open up. From this area you can get downtown on the route 10 or the 6 in about 20 minutes.
16th Avenue from downtown to Colorado Blvd has some real treasures. 16th has a great bike path and you can ride downtown in 10 minutes.
Moving north from 16th Ave there are several neighborhoods, some of which are the oldest in the state. Neighborhoods like Five Points and Curtis part are very fun places to be, but they are still very much transitional (or being gentrified, depending on your perspective.) I would consider living in these areas, but they are by every sense of the definition, inner city neighborhoods.
Apartment finding can be tricky here, and unless you're used to California prices, you will probably find it a little expensive. Just last summer the apartment vacancy rate in Denver proper was under 3%. That makes things hard, but hey, obviously this is a happening place and people want to live here