You can try Bharatpur. Bird watching plus relaxing at hotel (Birder's Inn is closest, in budget and very hospitable)
Hastinapur wildlife sanctuary near Garhmukteshwar is also nice.
You should try treking and camping...
Chopta trek
Valley of flowers trek
Kedarnath trek
churhdhar trek
triund trek
Denkund trek
kanatal : surkanda Devi trek
I think it would be better to visit places in Himachal or Uttarakhand given that generally may is very hot in the north.
any of the places such as Manali, kasol, dharamshala will be good options.
Uttarakhand also has good options.