What's your budget? My rule of thumb is, if you can afford it, live as close to the Opera House as you can. There's probably the largest concentration of shopping, (higher-end) restaurants and nightlife around that part of the city. I live in an alley off Le Thanh Ton east of Thai Van Lung and I quite like the neighborhood. You can just wander around the alleys and there's a good chance you will see signs for house/apartments for rent. Of course, you could always rent a posh serviced apartment as well but that will probably cost you over US$1000/month.
