We stayed in Ambleside last year, its pretty hilly! I got a local guide book and chose the “family ride” over to Troutbeck. Some parts I had to get off and carry 5 bikes (mine, wife & 3 kids) as some of it was like a waterfall without the water (heading up) We all made it round but it was hard work)
Biketreks is a good shop, but pretty busy so if you need any repairs they have the bits, but take your toolkit. They say they do hire out, but probably worth a call. There is another one tucked away in the backstreets (where I got the book).
There are some good rides around Grizedale, but make sure hes got at least 15 gears, my girls couldn’t get up some of the hills with 5. They have a hire / bikeshop at the visitor centre with a good range of bikes.