Agra can be done in a long day trip from DEL. Jaipur is a good weekend trip too. You can combine the two for a 3-4 day trip by car. Kathmandu if it is safe can be a long weekend.

Most every place is reachable by air from here and you could do on a weekend. However, be ready for flight delays. In Dec and Jan there is a lot of fog in Delhi and you will have even more flight delays and maybe some cancellations.

There is also a lot to see and experience in Delhi.

Sometimes it is cheaper to fly to Bangkok than it is to places farther south like Goa