We went to Tenerife to an all-inclusive resort when DD was 3 months old. It worked out fairly well. I'd highly recommend trying to find a place with a buffet style breakfast/lunch/dinner as one of you can watch the baby or walk with them, if they are antsy, while at more formal places, guests will get annoyed. However, DH said that it was still not as relaxing, as we didn't really get any couple time.
Look for places with a toddler pool area and a mini club - some mini clubs take kids as young as 18months old for a little while.
This summer we rented a cottage together with my parents-in law close to the beach. The self-catering was nice, we didn't have to worry about people in neighboring rooms, etc. The grandparents were happy watching DD while we went out with hubby to restaurant, movies, stuff like that. So, I think going with family / friends is definitely a good option.
As for country, I'm trying to stick to places where I'd feel comfortable to take LO to the doctor/hospital (God forbid) and I'm pretty sure that I could make myself understood.