Most hotels or motels allow you to check in without proving your age, but you may need a credit card.As a general rule most hostels allow teenagers. Youth hosteling web site says: Do Age limits exist? Youth Hostels are open to everyone. However age limits may apply for children in some places - check with the Hostel. Young people may be given priority when the hostel is nearly full. So try some of the other youth hostels around there. There are not many around but there are quite a few low cost hotels that take most walkups. Are you coming by car or do you need to stay within waking or biking distance of the beach ? My suggestions will also depend on your sex and vulnerability, but if you are confident you can figure out the safe people from the creepy ones try googleing couchsurfing.com or globalfreeloaders and you can stay for free.
Not all hotels require you to be 21. You should check around the area for hotels/motels because there are alot that only require you to be 18.