Beach Club Bistro is hands-down the best restaurant in Euclid. It is located in a small building in downtown Euclid and has two rooms: the "lounge" and the "dining room". There is also a small bar with five or six seats, but the real gem is the back patio, which is open during decent weather. The restaurant seems to do pretty good business, but it's usually not excessively busy. They take reservations but you probably only need one during prime time on Friday or Saturday.
The food is consistently excellent. I typically don't order pizza at restaurants because I feel like I can get pizza anywhere, but the Beach Club is an exception. The prices are very reasonable to boot. They keep a huge selection of wine as well as a diverse bunch of beers on tap. All of the servers are friendly and good at what they do. Definitely worth a visit.