If I need travel shots, can I go to local board of health?

Yes. Most local health departments will provide vaccinations for travel for a small fee.
Perhaps. Some, but not all, county health departments provide clinics where you can receive travel vaccines, sometimes at subsidized prices. Best to do your homework in advance. www.cdc.gov/travel is a good, country based, resource. Alternatively, visit a travel medicine expert to discuss strategy and learn what you really need.