OP said near downtown and near water. Shelter Island is roughly 1 mile from downtown.
The OP needs to decide whether s/he wants to rent a car or go car free. Shelter Island hotels are ideal with a car; not at all appropriate without. Downtown hotels are ideal without a car.
hiyo has recommended La Pensione. It is - or has been - the top rated budget hotel in San Diego in both Fodors and Frommers.