You’ll understand why so many people want to live in Prospect Heights after visiting this handsome little inn. First lure is the quiet, tree-shaded street, which despite its serenity, is within easy walking distance of fab boutiques and restaurants, as well as the Brooklyn Museum, Prospect Park, the Botanical Gardens, and subways into Manhattan (about a 20- to 25-minute ride). Next is the style of the place, which is oh-so-Brooklyn. Owner Billy Tashman, a former public school math teacher (he’s a very sweet guy), salvaged massive school science posters from the 1950s (on such topics as “Symbiosis” and “Evolution”); these give each room a quirky charm, which is further enhanced by the antique chandeliers, carved wooden bedframes, and lovely armchairs he and his designer bought, mostly on Craigslist. The final appealing element: the prices, which come in well below Manhattan rates, both for the rooms with bathrooms (and kitchens) and those without.