Uttarakhand in the month of june for trek can be done for following places:
Kedarnath which would cost 7k per head
Chandrashila trek which may cost 5k per head.
All I can tell you is to be safe since you are visiting Uttarakhand in late June, which means lots of rainfall and yes very high chances of landslides and other epidemics, so plan accordingly .
Be Safe
Thank You