You can explore it alone. just take a metro card and explore delhi in Delhi's lifeline THE DELHI METRO. IT will be fun. Also you can do it in delhi darshan bus. this bus will take you to almost all the historical places in delhi.
1 day to travel to Gokarna (Saturday)
3-4 days to check out local beaches (sun-wed)
1 day return from yana caves and yana rocks(thur)
1 day complete relax(Fri)
1 day to travel back (sat) Typically if you have your own diesel car it may cost you approx. 9000 @80 rs per litre avg and car giving avg of 15.5/ km Food could cost you around 1300/- per day Stay could cost you depending on your choice approx. 800 to 2100 per day Enjoy your trip. The itinerary is from Mumbai covering approx 1600km to and fro
If you are going to stay in or near Udaipur for 5-6 days I would recommend Day 1/2 visit all the local spots in Udaipur
Day 3 try to visit Ranakpur jain temple and kumbalgarh fort (127km so start early and be back by evening)
Day 4 try to visit eklinji close to Udaipur City and then nathdwara for its temples and huge lord shiva statue (it's still being constructed 44km away from Udaipur)
Day 5 try to visit Chittorgarh fort (approx. 115 kms from Udaipur) Happy travel and be safe please.
Old manali, Solang valley and Rohtang pass are must visit places but also these are crowded.
go for offbeat like joggini falls, beas kund trek and also some adventure activities like river rafting in Beas river and other activities in Solang valley like paragliding or skiing
You can visit Auli, Manali, Dalhousie. There are many hill stations in India where it snows in winters. You can go for Auli Hill station. It's a popular winter destination.