I wouldn't consider the Platt address, that is too much of a transitional neighborhood.
The Shaw address is between Fresno State and Fashion Fair Mall (about 1/2 mile to each), in the middle of a major activity and business area. I don't know enough specifics about that complex to help much beyond telling you the area has a high number of students nearby and also some low rent housing nearby.
Anywhere in Fresno is probably no more than a 20 minute drive or so from downtown. So you can probably expand your search.
Most of us on here suggest a couple of areas for apartments and condos.
If you want to be close to restaurants, shopping, health club, etc and are single then look into places near RiverPark, basically Nees Avenue from Palm Avenue to First Street (and nearby streets) in the 300, 400, and 500 blocks of East Nees. That is close to Highway 41 to get downtown.
A few of the complexes in that area to look at would be Windscape, River Park Place, etc.
Another area is Clovis, some newer apartments and condos are available within a mile or so of the intersection of Fowler and Herndon. They have easy access to highway 168 to get downtown (about 20 minute drive).
Downtown Fresno has been slowly improving for housing. But there are very few areas near downtown that I would suggest. It really is not an urban living area like New York, it still has few services and amenities available at night. Much of Fresno is based on a more suburban model.
If you really want to be downtown I'd suggest only looking at either the newer loft apartments by Reza Assemi (see the Urban Fresno site) north of the museums or a couple of cmplexes along Huntington Blvd like the Villa Borgata condos.
http://www.urbanfresno.com/
http://villaborgatahoa.com/index.html
Another area to look at would be rentals in the Tower District. That is the area around the intersection of Olive and Wishon. That is the trendy alternative area, probably the closest to an urban neighborhood right now. The area hosts events like film festivals, gay pride events, etc.