I spent 4 nights in the area in early summer 2018, specifically to explore the locality centred on Poschiavo by train. I was on a very tight budget, on an Interrail (= Eurrail) 22 day pass, and it made very good sense to stay in Tirano. The advantages were:
1) Much greater affordability - I had a basic budget en suite single hotel room for under £40 a night at the Hotel Corona, Viale Italia 19, 23037 Tirano - not fancy, but perfectly clean, pleasant and serviceable, and with breakfast included. Others were doing the same, staying in a variety of airbnbs and cheaper hotels in the town, and they were happy to be doing so while exploring the Bernina line. Savings here enabled me to have the occasional treat in Swiss cafés and restaurants
2) Shopping in Tirano is very cheap in a range of local supermarkets
3) a fabulous - and fabulously cheap - pasta and pizza shop El Trigo between the hostel and the stations
4) it's a compact little town, hotels very close to the two stations
5) The Swiss Travel Pass will take you over the border into Tirano
6) Any excuse to use my Interrail pass on the Bernina line train as much as possible for short trips to attractions such as the Brusio viaduct, the lovely Miralago and walk alongside the lake to the next station Le Prese, Poschiavo itself, and the fabulous climb on the train, with amazing views and a lovely series of local walks between Poschiavo and Alp Grüm, near the top of the route. It's about 40 minutes, sometimes less, on ordinary trains (approximately hourly) from Tirano to Poschiavo, and another 40 minutes from there to the summit. What views!
7) You can take a trip by train (2 hours) to Milano if you wish, though that's not on your pass.
The snaps show the lakeside walk between Miralago and Le Prese (view towards Poschiavo), the astonishing Brusio viaduct from that village, and on the walk from Alp Grüm down to Poschiavo that constantly crosses the switchback railway.
It was a memorable stay - I'm sure yours will be too
Hope that's a help