We've gone both ways with this!
Now that our children are a bit older (2.5 to 9), we typically do give the kids an early dinner, put them to bed, and then come back down for dinner. We don't have a baby monitor anymore, but our older children are quite capable of calling or walking the little ones over to us should they need anything. We've done this mostly in small boutique hotels / guest houses that were family friendly and that felt very safe. It's really not all that different from putting them to bed at home!
I personally think cranky, over tired babies or toddlers are far more disruptive than a baby monitor. Even with our school age kids, we're still practicing manners with a goal of having them really able to be sensible in a nice restaurant. Kids have to eat and we want them to enjoy dinner with our family, but we also try not to have them in nice restaurants after about 7:30 or 8:00 when all the kid stuff we're teaching them goes OUT the window.
I think the most important thing is safety - and you know your child best. I would also check with the hotel to see how they feel. We found that guest houses on our recent trip to Morocco were highly accommodating of children and families. Going down to have dinner and tea in the courtyard of our riad in Marrakech...and then having a drink up on the rooftop balcony...such an escape all while our kids slept! We also had our 4 children share a room and slept in the room next door to ours...again felt just like home, but only worked because the Riad was safe and family friendly.