Seeing that Birthday billing must be included in your trip I will suggest you go to Dharamshala. it's a beautiful place with Dhauladhars right in front of you. They beautiful clad mountain ranges are recieving snowfall as I write this. Birthday billing is relatively close to Dharamshala and regular buses or cabs are available from there. Also there are ample number of treks from Dharamshala the most famous one being Triund, Kareri, Dal lake, Nag Dal. Dharamshala has HPTDC hotels which offer great service with minimum prices. From Dharamshala one can also do paragliding, parasailing. Excluding the cost of travel from Mumbai to Delhi, I would say a minimum 4 day trip would cost you around 7-8 k excluding the paragliding. If you want to do adventure sports please look up adventure operators before hand and confirm the rates. Please be very to carry some extra cash in your pocket as adventure activities at Bir Billing are costly.