You will want to contact the motel directly before traveling. Jasper is very close to many areas that were directly hit by tornadoes. Some areas are not expecting power to be restored for 2-3 weeks. Also, as you mentioned, many people will be using motels because of damage to their own homes.
To help you decide if another place will be best, may I ask the purpose for your visit? If it is an activity or event in the Jasper area, you may need to plan to stay there if possible because there aren't many other options within an hour or more from there. Visiting family? May need to plan to stay with them.
As far as needs, there will be a need for many weeks (maybe months) for basic household items, bottled water, toiletries, batteries, etc. One option would be to contact the Jasper Chamber of Commerce to see what needs they know of before you leave. Here is their website with contact info: http://walkerchamber.us/
Other websites to check:
www.helpalabama.com
www.toomers4tuscaloosa.com (this site includes information on all affected areas, not just Tuscaloosa)