If your budget is 250 USD, you would have a good range of choices. Most people would recommend staying in in the 4 and 5 star establishments in the Marina area, Orchard, or Clarke Quay.
Most of the well-reviewed hotels that's within your budget according to booking.com, Asiarooms, and Zuji are: (And I really think that these hotels are great, having stayed at most of these places myself)
Fairmont - great location atop a good mall, grocery store, department store, and MRT station. Near Chjimes for dining and late night drinks. Right beside Swissotel Stamford, but I prefer Fairmont as it is more exclusive and definitely less crowded.
Royal Plaza on Scotts - right in the middle of Orchard, with access to buses, MRT, and about a dozen malls, and great restaurants.
Swissotel the Stamford - also well reviewed, right beside Fairmont. Also good, but I really prefer Fairmont. Request for a high floor with bay or river view. Good watering holes at the 70th floor.
Goodwood Park - very near Orchard, but not quite in the middle. Very good option if you want a place that's central but feels more quiet.
The Regent - managed by Four Seasons. Old, but I still like the lobby, and the rooms are still up to par. Good service too.
Swissotel Merchant Court - one of the most popular here in TA. In Clarke Quay, near MRT, nightlife, a lot of restaurants, and by the river. Fantastic location, and very good reviews.
Rendezvous Hotel - at the end of Orchard Road, good location near MRT, National Museum, restaurants. Newly renovated.
Carlton Hotel - right in front of Fairmont, Swissotel Stamford and Chjimes. Also great reviews, and a TA favorite.
Mandarin Orchard - right smack in the middle of Orchard, in between 2 MRT stations and a dozen malls.
Grand Park Orchard - newly renovated. Haven't tried this hotel yet - the reviews are mixed, but generally good. In front of Mandarin Orchard.
The other hotels that are fantastic, probably better than some on this list are: Mandarin Oriental, Marina Mandarin, Pan Pacific Hotel, Conrad, Ritz Carlton. As of now, the price is above your set budget. However, if you see a promo or sale, or if your willing to go up, then definitely go with one of these (especially Mandarin Oriental or Pan Pacific Marina).