Can the hotel booking API find hotels near a place my customer names, like a beach or a conference centre?

Yes, most hotel booking APIs can search around a point on the map, not only by city name. If you know where the beach, the conference centre or the hospital sits, you can ask for the hotels within a set distance of that point and get back the properties in that area, usually with the distance from it shown against each one.

There is one step you have to handle first. The supplier expects a map position, so your search screen needs to turn the place your customer typed into that position, which is normally done with an address or map lookup service behind your site. Some suppliers also accept their own landmark or district codes, and those can be handy, but the lists differ from one supplier to the next, so searching around a map point is the method that tends to work everywhere.

Be aware of what it cannot promise. The results are only as good as the address the supplier holds for each hotel, and while most are right, some sit a street or two away from where they really are, so a genuinely close hotel can be missed. The distance you see is measured in a straight line as well, not by road or on foot, so somewhere that looks close can still be a long way round. Suppliers may also limit how wide an area you can ask for.

A sensible next step is to ask your supplier whether searching around a map point is available on your plan and how wide an area it allows, then try it on two or three of the landmarks your customers ask about most and check that the hotels you would expect actually come back.