You can opt in for hostels, they're the teenagers preference in Manali. Lost Tribes in Jagatsukh, Zostel in Manali & YHAI Manali could be some of the places with like minded people & at very affordable prices along with better amenities.
If you're going in off season then you can directly walk in, but if you're going in peak or mid season, then I would strongly suggest you book in advance. Most of them can be booked online on their official sites or some other travel aggregator.
If you want to enjoy the adventure sports then you should directly head to either Bir or solang from Manali as they are kinda den for adventure sports.
The easy commutable place to stay in manali is New manali as you close to all the auto stands and bus stands but if you want to enjoy the fun vibe of manali and bare a bit of walk then should go to the old manali part (differs person to person)
If you planning during this time, then nothing is possible. Make your plan during Summer. If you have fully 2days, then on very 1st day go for Hidimba temples, johini waterfalls, Manu Temples, Beas River. On 2nd day go for Solang vally, Gulaba. You can try Paragliding at Solang. Then you can go for Rotang Pass. But if you going this time, then Solang, Gulaba, Rotang are closed now.
2 days are less for manali
stay at vashisht,beautiful and calm place with good food,.
take 1 day for local sight seing like,mall road,hadimba temple,van vihar and club house.
day 2 for solang valley for adventure and snow activities
U can go to solang nalla , it is around 15km away from Manali and it is a very beautiful place . You can do paragliding ,and so many places to visit nearby like anjani mahadev temple. In Manali ,you can also go for rafting, trekking and hampta trek is good. Dhundi is also a very beautiful place in Manali ...you will definitely love the view .
You'll find a lot of places on mall road..
you can also try staying at zostel beas river rafting and paragliding done in manali itself or you could visit to solang valley for more adventures
you can also visit rohtang pass, gulaba snow point and hadimba temple