In the USA, you can go to local nurseries, big box stores (Home Depot, Lowe's, Walmart). Whenever you travel stop at some of the local nurseries (and big box stores) there as well as their stock may be different than your home town. (I picked up a nice Chirita 'Moonwalker' in Hawaii two years ago at the Kona Walmart for example)

You can order online from Steve's Leaves, Taylor Greenhouses, Kartuz, Logee's, eBay, The Violet Barn, Accents for Home and Garden, and I'm sure there are some other smaller but good places to buy from. Unfortunately there have been some closures of mail order places in recent years. There are some I would not recommend but won't mention their names here.

See if you have a local begonia club in your area (go to Begonias.org and then click on the Branches tab (fourth from the Home tab). Scroll through that page and see if any of the branches are close to you. If so, contact them and find out where they meet at and when.

Go to the annual ABS convention. It is kind of an expensive way to buy begonias due to airfare, hotel, food, etc. but you will have a huge selection on sales night (Friday night) at very reasonable prices, meet like minded folks, see some great gardens, and see some great show plants. You will have to be an ABS member but it is a worthwhile small investment ($25). This year's convention will be in San Antonio May 3-7. They are combining the SWR (south west region) get-together with the ABS convention so it should be a double treat in a way.