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Plenty of hotel apartments in Bur Dubai within your budget which have outdoor pools and are close to the creek - I can't remember specific names but have a look on Booking.com. There's also the Arabian Courtyard Hotel near the creek which is nice, you might get it for $150.At the beach, there are several hotel apartments in Jumeirah near the Mosque. The beach is across the road. Also try renting an apartment at Jumeirah Beach Residence. Otherwise, hotels in Satwa such as Jumeirah Rotana or Ramada are within 10-15 mins walk of the beach.
