This may help with the restaurants http://www.yelp.com/search?find_loc=...lt=restaurants

In the area you are staying in it is safe to walk around...on the outskirts of Downtown it is not but you can easily see where it is safe and where it is not.

The YMCA in Downtown is suppose to be really nice...really http://www.yelp.com/biz/ymca-of-metr...-los-angeles-9

This website may help too to walk around and check out the sights in Downtown. www.downtownlawalks.com

[BTW...yelp is my other BB that I belong to and I have met many yelpers and I trust their recommendations]