What is budget? The top ones are all in District 1, the Caravelle, Westin, etc.
My favorite is the Somerset Apt, there are two locations. The newer one is next to French Embassy, one or two bedroom apts for the same price (or less) than 5 star hotel. I paid about US$120 last visit.
Has nice pool, small gym, but no room service. Bkfst is available in small cafe/bistro next door, small grocery store also. Room is full size apt, has full LR, DR, even washer/dryer, full kitchen, free internet. Excellent security, long term stay for many expat families - school bus in early morning!
Somerset is about 1 to 1.5 miles from Caravelle and all the restaurants....I've walked in evenings and completely safe area.