Side Farm in Patterdale goes right down to the shore of Ullswater and is in a v beautiful location. Gillside Farm in Glenridding is right on the beck, and also in a great location. Details of both here
I have walked through the langdale site and it looks lovely.
I stayed in the nt site in langdale 15 years ago and it was very rowdy. A group of teens turned up after pub closing, pitched their tent by car headlight and got the guitars out. Afaik there is no staff on site overnight. However they were evicted the next day and it was quiet after that.
we went to Park Coppice in 2008. it rained the whole fortnight we were there but the site was lovely and drained well! I notice it has been refurbished since then but was quite good when we went so don't know what needed refurbishing. Its right near lake Coniston and you can walk to Coniston itself in about 20 mins iirc. Quite a big site but was quiet
Rydal Hall is a lovely site. Numbers are fairly strictly limited so it's never too busy and is never noisy. Walking distance to Ambleside and Grasmere. Beck to paddle in and small play area. It's just lovely.
NT campsites at Langdale and Wasdale are great. Wasdale NT site has little streams all around for children to paddle and dam in, and trees to climb.
We also often stayed (before we movcd too far to go for weekends) at Side Farm at Ullswater, also Coniston hall campsite, both of those are right by the water if you do watersports (or have toddlers who like to pootle on a beach). Coniston hall gets very noisy though.