@michelesussexyoga
Welcome to the expat.com forum and good luck with your property search!
The Black Sea coast is very pretty and there some very nice towns and villages that you could pick. But it depends on how close to the coast/beach and how close to civilization (large town/cities) you want to be (and how big your budget is). Distance from the coast affects the price a lot, if you're happy being 50 km (or more) inland.
The main cities are Varna and Burgas, so I'd personally prefer to be close to one of them. Near Varna there are small towns like Byala, Balchik and Kavarna while near Burgas you have Sveti Vlas, Nessebar, Pomorie, Sozopol, Primorsko, and Lozenets. You can find village properties in/near them.
Sunny Beach (between Sveti Vlas and Nessebar) is the largest summer resort in Bulgaria, so it's packed in summer. Sunny Beach itself is mostly apartments, but, for example, Kosharitsa is 3km inland and is a popular spot for villas and houses. Still a bit too seasonal for my taste, but it might appeal.
If nature is important to you (apart from the coastline itself), there are wetlands up north (Durankulak), around the Burgas Lakes (and Pomorie Lake), and further south (Ropotamo). I like Sveti Vlas because this is the easternmost point of the Stara Planina, so you have some very nice hill walks here. Down south we also have the Strandzha Nature Park.
Trying to narrow it down to specific locations is quite difficult. I'd suggest it's perhaps easier to search for properties in the coastal region, and see what (if anything) appeals for your budget. For research, I like BulgarianProperties (even though there are lots of other agents) because they have plenty of listings (in English) all over Bulgaria, and they're usually quite informative (detailed descriptions, plenty of photos, sometimes 3D interiors).
Here are their current houses/villas in the Burgas region:
https://www.bulgarianproperties.com/Search/index.php?sadx=1&stip_text1686080404=&stop_text1686080404=&stown_text1686080404=Burgas&sdevv_text1686080404=&minarea=&maxprice=&skeyword=&spredlog=innear&c=Search&stip%5B%5D=43&stip%5B%5D=19&stip%5B%5D=52&stip%5B%5D=51&stown=282&srtby=2
For comparison, here are the Dobrich (35km inland from Balchik) listings:
https://www.bulgarianproperties.com/Search/index.php?stown_text1686470135=Dobrich&squarter_text1686470135=&stip_text1686470135=&minarea=&maxprice=&skeyword=&sadx=1&sady=&spredlog=innear&scntr=1&c=Search&stip%5B%5D=19&stip%5B%5D=43&stip%5B%5D=52&stip%5B%5D=51&stown=544&srtby=2