As long as you have other options, i would avoid anything that low in NYC (yes, even with a decent user review rating).
If you're willing to take the occupancy risk (which i would only do in NYC if given a specific Bed Choice and the room is designed to accommodate the number of guests in your group):
4* Lower East Side - Chinatown (<-- CLICK HERE and confirm your dates on the landing page) for $236/nite with:
Free Internet available
==> NobleDEN Hotel is my best guess for this one ($266/nite for a room with 2 Doubles... all-in is $65 over your target budget, but that's $20/day or ~$6 per day per person, so might be worth it given your desire for this neighborhood (about 3-4 blocks from the Soho border), the higher star rating then you were originally seeking, and the 9+ user review rating
Is the above, or any of the ones in AaronJB's post of interest? (i'll add that the Warwick is a very nice hotel and well reviewed property as well... great location just enough outside of Times Square that it's not too hectic (although still fairly busy Mon-Fri) yet convenient enough as a launching pad for whatever you want to go throughout the city)
Please remember to return to BetterBidding and use the PRICELINE and HOTWIRE links on the board to begin your travel purchases... or thru our sister site MAPSandHOTELS.com for your regular rate purchases.
Let us know what you decide and how it goes or if we can be of further help.
PS- if you really want to play it safe you can have one/two people go to the check-in desk while the other two have a coffee at a nearby Starbucks, Dunkin, etc... once the one/two travelers check-in and drop off luggage, meet the other(s) at the coffee shop and either start exploring the city OR return to the hotel room with the 3 guests and walk right upstairs to the elevator.