It all depends on your Mood, like what would you like to explore? For the Historic and Cultural trip you May Visit
Rajasthan For Some Sort of Adventure you can go to
Dal Housie If you want to go raw and explore the natural beauty you may go to
Nepal or the Hill stations like
Lavasa If you're planning a Budget trip then Goa is a bit cheap around those Months so you may Give it a try as well. If you're Interested in Safaris and Animals, you may go to
Jim Corbett National Park
Ranthambore National Park
Bandhavgarh Tiger Reserve
Gir National Park Since all of the National parks in India are usually closed from July to October. You can plan this as well.
May is generally Hot, so avoid any kind of coastal or south indian places.
In North, you can explore:
Rudraprayag & Devprayag
May is the start of summer vacation and most of the people are looking to go for a summer vacation and choice of destinations usualy are cooler places, especially hill stations up north. so if you want a good peaceful vacation and not be buried under people, places like Coorg and Munnar or any such hill station down south would be better. if you don't mind some humidity, and want to enjoy nature and luxury at its best, you can try Goa as well. it will be hot and humid, but you get top hotels at very good bargain and once the rain starts, it's very beautiful. so you use early morning and evening to venture out and enjoy the noon, in the luxury of your hotel/ resort.
If you wish u visit heart of India I will suggest
Orchha and Gwalior in Madhya Pradesh when visited them I really felt they are hidden gems u can go through my write up to know more about both the places at https://travellingfeets.travel.blog
If you're a trekking and hiking enthusiast like me , you can visit
Har ki doon trek (uttarakhand)
Kashmir great lakes trek
sandakphu trek (India Nepal boarder)
kalpa and chitkul (Himachal Pradesh)
tirthan valley trek (Himachal Pradesh)
Nanda Devi (binsar - Himachal)
mangi - Tungi (Maharashtra)
sarahan (pilgrimage- Himachal Pradesh)
chakrata - uttarakhand
sainj valley - Himachal if you are planning in North India dalhousie
sikkim if it's in South India
Andaman if it's in North East
cheerapunji hope it helps you!