Planning January trip 3 weeks

I am just starting to plan a trip to India in January - was hoping to go for a month but my husband can only get 3 weeks off(which will end up maybe a day or two less depending on our flight from NY). We want to visit Agra(missed the Taj on our first trip if you can believe it), Varanasi, possibly Bodhgaya, Mumbai, Shirdi, and a couple of days shopping in Delhi. We are on a rather tight budget so were hoping to only fly from Delhi to Mumbai, everywhere else by train. Are there any other places we should add to this skeletal itinerary - these are just the 'must sees'. Originally I really wanted to visit Madurai/Meenakshi mandir but it is so far from everything else on our list - think we will have to save the south for our next trip or else scrap this itinerary and just visit the south - just trying to get some ideas. I am hoping there are some peaceful natural places we can visit to relax to get a break from the cities.

A hundred kilometer from Shirdi is Aurangabad, next to the caves of Ellora and Ajanta and the fort of Daulatabad.
In the city is the Bibi ka Maqbara build in the same style as the Taj Mahal.
You can go by train from Varanasi to Agra.
From Agra there is an overnight train to Aurangabad.

In three weeks don't try to do North and South both.

My honest opinion is skip this and go South....a number of reasons;

1) Firstly, in January, the weather in the south is excellent and the best time to visit (especially coastal parts of Kerala, Tamil Nadu and even Goa and the Andaman Islands as well as cities and hill stations.

2) The South is much, much smaller than the north and the roads generally in a lot better condition. This means with 3 weeks, you'll get to see a lot more and travel a lot less.

3) The distances in the North are huge, the roads terrible in a lot of places and train distances long. Your post indicated/alludes to the fact you'll be making a return trip to India in the not so distant future. I would wait until you're there for a longer period of time for this trip!

I know all this first hand as I've spent a lot of time in the South and quite a bit in the North. Add to that I'm currently planning a similar trip to the one you mentioned and although lot's of the distances are only 100km because of road conditions and limited trains they can still be 7-8 hour journeys!

NB

Thanks - sorry for replying late to my own thread. If we are most interested in natural places(NPs, gardens) and temples, not really beachy types, which places would you recommend? We were hoping to keep the flights down to one because of cost limitations. I remember well from our first trip in the North how long some of those bus/car trips were! Weather is definitely a factor as we will be coming from chilly NYC and want to cheat winter a little bit.