I agree with mamashtakeh – the premise of your inquiry reveals your ignorance. What makes you think that teenage girls have any inherent right to have fun?
Seriously – there is not just “one” fun thing to do – there are many fun, and safe, and tznius, things to do – you need not do the same thing every week, mix them up –
1. ice skating
2. rent a movie (plenty of appropriate fare out there)
3. get a board game or similar (Apples to Apples, Would You Rather, Pictionary)
4. get a pizza and meet at someone’s house for 2 or 3, above
5. go to someone’s house and make your own pizza
6. go for ice cream
7. call the local social services agency and be a “big sister” for a kid on a Saturday – I’ll bet a ton of service agencies would be glad to find some mature, level-headed young ladies to be a “big sister” for pizza and games on a Sat nite
this is not an exhaustive list – but the important thing is to maintain your committment to “kosher” fun, and to be safe while doing so