We have stayed at the Doubletree @ BG many times. It is my second favorite hotel in the area after Embassy Suites and those 2 hotels are the only ones in the area that are rated 3 stars by Priceline. The hotel is about as close as any other in the area, close but not walking distance. BG is located within the square formed by Busch Boulevard, 30th St, Fowler Ave, and 40th St.
The Doubletree is next to AmeriSuites (DO NOT go to Amerisuites!) on 30th just off of Fowler. If you have a car the best way to approach the park is to make the left out of the doubletree parking lot, make a right onto Fowler, go one block and make another right onto 40th. The actual park entrance is on 40th, and by going that way you beat the majority of the crowds which tend to get backed up on Bush Boulevard. Whole trip is about a mile. If you don't get there early pay the extra 6 bucks for preferred parking it's well worth it.
If you do not wish to drive I think they might have a shuttle but I am not positive on that.
The hotel itself is all suites. (real suites with 2 TV's not what Amerisuites calls a suite LOL) It's not a new building, but it is clean, the rooms are spacious, fridge, micro, sink, dining table, nice toiletries, comfy and QUIET a/c units. There is a small but nice pool. The layout is courtyard style with hotel key access from the parking lot after dark. As far as the neighborhood, I would not go for any long walks after dark, but then there is not much to walk to in the immediate area other than the restaurant next door. Once when I had a ground floor room I thought I heard someone outside my back window and when I called the front desk they sent a guard within 60 seconds to check it out. I have stayed there many times since then without incident, and I am a single Mom with 3 kids- no worries.
They used to offer free breakfast of eggs, toast, hashbrowns and some dry cereals, donuts, fruits and the usual beverages. They now charge $3 per adult (kids are still free) and that's still a good deal. There is a nice family restaurant right next door ( I believe it's called the Village, but I may be wrong) in any case it's like Denny's or Perkins style food, and open early til late.
Sorry this got long, but I hope it helps- and BTW- Don't forget to ask for your cookies when you check in- they are big warm chocolate chip cookies and they are VERY good!