You can get right outside Bayside at the Clearview Gardens. 2 Bedrooms go for around 220, I think, and they are basically all Garden Apts. The Q16 and an express bus is up there, the Cross Island Parkway is up there, so is the Clearview Expressway, and Clearview Golf Course. Bay Terrace Mall is nearby, and there is a smaller mall near Fort Totten Park,, which is a nice park, btw.. It has great elementary schools, and a nice view of the bridge. My son goes to school at PS 209, one of the best in NYC- the non alpha fourth grade passing % is in the high 90's I believe.
The only drawback is that if you want Bayside because of the LIRR access, you won't be anywhere near it.
Good Luck, Antolin