if you dont' mind the 2-3 block walk you can always park in the Hilton parking garage. that what we normally do. Keep in mind there is not a lot of places that allow for self parking... Most of them are valet parking. And you have to pay for it. The Marriott on Canal is super nice...they are at the top end of your budget. And they valet park, but its not free.
check these out...these look in your budge and are pretty good hotels: