narjee - I've done what you're planning (scouting other places and bargaining) - and was no problem. One thing you should consider - remember you'll have to check out by 11AM and that's not much time to find a place (depending what time you arrive first day), especially if you're up late Friday night. And you won't be in a good bargaining position dragging your suitcases with you and asking if they will give you a deal. You'll have best luck bargaining the longer you stay - i.e. ask if they have a weekly rate.
So I usually book 2 nights when I do what you're doing. You won't get much done arrival day and will most likely get there later than you think. With 2 nights, you'll have the whole next day to find a place. Then check out at 11 and move the next day.
That said, two doors to the north of Roots is Fun Holiday. They are budget hotel in your price range. Also, I looked at Pure Gardens this trip, for later - it is also same price range and looked better than years past since is under new mgmt - but is across the road from the beach. Not really a problem, because Bourbon Beach is across the street and sort of caters to day-trip beachgoers. So does Mama Flo's and Sunbeach Bar.