East Europe is wonderful in summer. You haven’t mentioned where in India you’ll be flying out from but from New Delhi, Finnair has direct flights to Helsinki. Finland is an expensive country so stay in Estonia’s capital Tallinn instead.
You can stay in Helsinki for a day or two (hostel dorms from about â¹1,700 a night), then take the ferry to Tallinn. There are plenty of hostels in the Old Town area. You will find hostel dorms across Latvia, Slovakia and Croatia at reasonable prices (about â¹900 onwards).
In Estonia, I’d strongly recommend you go to Lahemma National Park, Hiiumma and Kihnu apart from trips to Pärnu and Narva (from where you can see Russia). In Latvia, you can visit Riga, Jurmala and maybe Cesis. In Slovakia, experience Bratislava, Devín, the Slovak Karst region for caves, and Košice. In Croatia you must visit Zagreb, Split and Motovun.
I’d suggest taking buses because they are the cheapest form of transportation (flixbus.com/ getbybus.com) to cross countries. In a town or city, you can hire bicycles or walk. Most intracountry travel can be done by local buses. Since you’re on a tight budget, try to keep meals within ¤10. But do try regional specialties. If you book your air and bus tickets in advance, a month on a budget of â¹1,70,000 should be manageable.