5 days won't give you enough time to go too far from Ho Chi Minh city (unless you want to book a cheap BL flight to Da Nang, then head to Hoi An for a day or two). Also keep in mind of the weather, it's the rainy season in Southern Vietnam, so it could get really wet. Bring an umbrella or get a rain poncho when you're there.
Places to stay in District 1: My suggestion is to stay at a small boutique hotel (tons of them), priced at around $30-$50 a night, including internet and breakfast (check on tripadvisor and pick the one you like). Wotif has some very good deals as well.
To get to the hotel from SGN airport, it's best to book and pay for a taxi at one of those taxi counters (at 7 USD to hotels in District 1) as soon as you get out of the terminal. If you don't pre-book, it'll take you ages to wait for a taxi outside. Also, the vast majority of taxis in HCMC do not accept our credit cards, only cash.
Suits: I've recently had some done at Son Veston (226 Tran Quang Khai street, District 1) for $200 each (jacket and trouser) - could be cheaper if you want to. If you're after better types of fabric, the prices can be as high as $500. Noting you're only there for 5 days, you might have to pay extra for them to rush it (it normally takes a week, including a trial before they finish the suits). Son Veston is one of the most popular tailors in the city (they also accept Visa or Master cards). There is another good one next to the New World hotel, but I haven't been there.
Have fun in Vietnam (and have fun crossing the roads too

)! It's a wonderful country with excellent food, beautiful scenery, and friendly people.