Chances are good that you can. Try to go during the off-season, especially in July and August, when rates and airfares are at their lowest. Twin beds cost more than a double, and any room with a private shower will be less than one with a bathtub. Back rooms often face blank walls or dreary courtyards and are usually smaller, but they cost less and are quieter. Inquire about the hotel's refund policy in case you send a deposit and then have to cancel at the last minute.
Some smaller hotels have draconian ideas about refunds.
If you have booked an apartment and paid a chunk of money in advance, are flying charter, or have a nonrefundable and nonchangeable airline ticket, seriously consider purchasing trip insurance. If you have to change dates, interrupt travel, or cancel altogether, you will be grateful for it. The Automobile Club of America has a list of carriers. Always check out the room before you check in. Avoid eating breakfast at your hotel if you want to save money.