Lucky you !!
Assuming you are going to Agra (and you can't not visit the Taj Mahal

), then the bird reserve at Bharatpur (aka Keoladeo Ghana Natiuonal Park) is on the Agra - Jaipur road and not far at all, and well worth a visit. Bit short of tigers IIRC though since a big drought.
Spent a magic day there (would have like three). Take a guide in a horse drawn carriage as it can be vvvv hot, and then walk when approriate. Found our guide to be very knowledgeable and a quick spotter.
The guy who did the organizing for me also had us staying the night before in a wonderful small hotel in a tiny village - very Raj, very rural, and very poor village. Absolutely magical. I've forgotten the name of the hotel though, but could easily find out if you wanted. There is an hotel in the park too.
Are you doing your own thing, or on a tour?
If you are doing your own thing then try and stay in small B&Bs when you will see the true India and not help the rich to get richer

Avoid too many trips to "red forts", of which there are are a huge number, as after the third you forget what each one was like. DO visit the red fort at Agra though, nice views of the Taj, and it is the fort that the Mumtaz Mahal lived in before her death and transfer to the Taj !!
Do take a train ride, bus ride, motorized rickshaw and do eat the street food - it is fantastic - many silly books advise against all of these
Ask locals where the best restaurants are - some are mind-blowing in their quality and service.
Please don't wear shorts as it offends many, but they will be too polite to say so. Hire a car with driver and not self-drive

Don't give to beggars - if you want to give, give to the temples or mosques who have freeding programmes and "controlled" charity. Many Indians have told me that there is no need for people to be hungry on the streets, as food is available through temples etc..
I have bird guides etc. if you want to borrow - pm me.