Can you find green tea and black tea in your local grocery shop? Like ralphs, albertsons, walgreens?
Generally nicer grocery stores stock a variety of teas.
The tea isn't always the highest quality; for the best stuff you generally have to go to nice tea stores or buy on the internet.
As far as cheap green teas go I'm a fan of Mr. Lee's Tea. It is an inexpensive Chinese tea with a mild and appealing flavor. It is very commonly served in Chinese restaurants here. Stores with Asian food sections often sell it in big boxes of teabags for a few dollars. I like it much better than Lipton, Bigalo, Celestial Seasonings and American brands of green tea.