Be carefull.Backpain can bother you in low capacity bike otherwise 250km is fine.
i have seen travellers doubling in 100cc bike and travelling in tough route of Hemkund sahib in Joshimath.So,there is no limit.
I have been to Mussoorie on my first Solo trip from Delhi. Other options include Agra, rishikesh, Lansdowne etc. 100 cc bike would do just fine on these locations. I've published a Mussoorie solo trip as well. For affordable stay ideas, contact me.