$700 or less for a one bedroom;
- Washington Square
- Greektown Lofts
- New Cadillac Square
- Claridge House
- Harmonie Park Lofts
- Fyfe
- Park Apartments
- Milner Hotel
- The Leland House Apartments
Those were in order from best to worst, although I suppose it's all relative. If Lafayette Towers wasn't up to par, other than on location and price, you probably will only find the first few on that list acceptable.
Kales, Lofts at Woodward Center, Millender Center and Riverfront Towers have apartments in the $700 - $800 range as well, and offer more luxuries.
Detroit's Downtown/Central Business District [[CBD) is one small district, it is surrounded by Corktown, Midtown, and Lafayette Park, which are walking distance to the CBD.
PS: Be sure to check out any hidden fees [[parking, keys, utilities, on-site facilities, etc.).