hey Nichelle,
Welcome to our country...!! that's great! The best possible option I can suggest is visit n try to book things in advance.
16th Feb - Arriving Delhi
17th - Delhi to Agra
18th - Explore Agra and try local cuisines and meet locals
19th - Come back to Delhi
20th - Explore New Delhi
21st - Delhi to Corbett (one of the best and nature lovers place, national tiger park) - 4-5hrs drive from Delhi
22nd - Explore Jungle and Safari's...
23rd - Visit Marchula (place of heaven and beautiful and next to Corbett Park itself)
24th - Corbett Park - Nainital ( Nainital - city of beautiful lakes and best time to visit these days)
25th - Explore Mountains and few other places around
26th - Visit near by temples and places like Tea Garden and stuff
27th - Come back to Delhi
28th - Leave from Delhi - Jaipur
29th - Explore Jaipur
30th - Explore Jaipur
31st - Jaipur - Pushkar
1st - Explore Pushkar
2nd - Come back to Jaipur
3rd - Flight from Jaipur.
I mean this could be possible your best itinerary and can explore a lot...
Need any assistance or any help with regards to booking or a nice travel companion surely can revert me back and will connect it accordingly.
I am from New Delhi only and a well traveled person around the globe.
Let me know if you need any help.
CHeers
Ady