After a very small amount of research, you should be able to find a lot of good options for you and your pet. After you have found some options, it's time to start weeding through them to find the best one to fit your needs.
Make sure to find each hotel's specific pet policy, either on their website or with a quick phone call to the hotel.
Different hotels, such as pet friendly hotels, will have different policies as to the:
size of the pet allowed,
a possible extra deposit required to have a pet stay in your room, etc., so make sure you know exactly what the policies are before you book a room.
Some helpful questions to ask each hotel ahead of time include:
any limitations on the size or breed of the dog,
and also what exactly the pet deposit covers.
Some hotels will be very strict with that pet deposit, and others will be more lenient. Make sure you know exactly what is expected of you if you stay at that hotel.
Once you have pared down your list some, you might be trying to figure out the best way to find good deals on hotel rooms that allow dogs. If you know of a specific chain of hotels that allow dogs on their premises, and their pet policies work well with your situation, you can always do the more traditional hotel searches, using a discount website like Hotel Planner or Priceline.com, or you can also try that hotel's own specific website.