I'm still in the early stages of my PPL, but we seem to average around 5000ft.
You're unlikely to go above 6000' during training.
The lessons you end up high are:
1. learning to climb - you'll only end up very high if you just don't get it. I once ended up at 9000' with a student who took longer than normal to get the level off properly.
2. Stalling/Spinning - 6000' is plenty to stall or spin most aircraft safely
3. Nav over high terrain - unless you've got some very high ground in your area, you won't end up above 6000.
On a lot of club aircraft the heaters aren't great, so the instructor may not want to be going any higher than this anyway.
It takes a long time to climb well above this in most club aircraft, but it's certainly something to experiment with once you've got your licence. It's one thing reading about a service or absolute ceiling in a book, it's quite another flying up to it and seeing how the aircraft behaves.