Laughing at Bowness being compared with Blackpool. OP, they are NOTHING like each other! 
Yes, Bowness can be busy in the summer as it's the first place that many day trippers from Liverpool and Manchester go. Geordies tend to go to the N Lakes.
I would not go anywhere near Blackpool, it's not my kind of place at all. But I do enjoy the hustle and bustle of Bowness and it's where I would stay with children who got bored by too much peace and quiet. We go fairly often to the Lakes and always like to stay around Lake Windermere. We have stayed in various types of places both self-catering cottages and hotels over the years, basic and fancy, all round Windermere.
The last few years we've stayed at Waterhead (walking distance to Ambleside) in a couple of different hotels. It's less busy than Ambleside or Bowness so quiet at night but a bit of activity during the day with the boats coming in and out. We like the relaxing atmosphere there as opposed to Bowness. A couple of hotels and pubs (beer gardens overlooking the lake) and tourist shops. Kids are nerdy mid-late teens so we are not after wild nightlife. It depends what your kids are into. We like a good long walk and then a sit with a drink in a nice pub overlooking the lake (kids on phones usually ha ha while DH and I chat.)
You need to bear in mind what you want to do in wet weather, and what the kids will be happy with. We've had some nice holidays in picturesque cottages in decent weather but a couple of short breaks where it rained for 2 days solid and none of us fancied walking in torrential rain so we were stuck inside the cottage playing games really which we could have done mich cheaper at home"! So hotels are good if they have leisure facilities. Low Wood Bay has been all done up, expensive though.
There is something lovely about sitting watching the lake with a drink. Some of the hotels have lovely views from their windows while you sit and eat eg the Beech Hill hotel, which is near Newby Bridge. Lakeside hotel is in a good position and there is an aquarium and steam railway (Lakeside and Haverthwaite)
My kids remember the walks the most. We've been up Catbells when they were younger (near Keswick) and closer to Windermere we've done some lovely walks straight from Windermere Village and Bowness. We also enjoyed walks around Tarn Howes and Coniston, Easdale Tarn and Grasmere. Wray Castle is worth a visit as is Brockhole (good tree trekking place, crazy golf, canoeing etc).
DH and I have enjoyed Blackwells (Arts and Crafts house) and Townend National Trust cottage at Troutbeck. Not sure kids would be into those though. DH only just tolerated them.
I love the Lakes, I feel at home there.