The SDY station is 1 block from the main street and downtown. Directly across the street from the station is/was (a few years ago) a Burger King. Just for comparison, ALB is not in Albany but actually across the Hudson River in Rensselaer. There is nothing nearby.
Schenectady has a new casino along the riverfront. I'm not a gambler, but I have stayed in the hotel that is attached to the casino. The biggest disappointment with the casino was the food. It left a lot to be desired.
Although I do like Albany, at this point I prefer Schenectady for my Amtrak overnights if I have a choice, largely because the station is in the center of the urban area and everything I could need is nearby. The downtown area seems rather healthy with very few vacant storefronts, while downtown Albany lacks much life after all the workers go home to the burbs.
A note on the Ethan Allen - on Saturdays it leaves Rutland late, at about 11 AM, so if transferring to the LSL eastbound your wait is less than half an hour.
If you like historic districts and walking tours, the Stockade District in Schenectady is walking distance from the station. It has a terrific collection of old homes from colonial to Victorian times, well-preserved, colorful and worth a visit. There is a guided walking map available online and a cell-phone tour.
For food, oddly enough there is a terrific Moroccan restaurant called Tara Kitchen. Also a favorite for lite fare and coffee is the Moon and River Cafe. It's a very eccentric place with music at night and friendly locals. Finally, next door to the station is a very decent Irish pub, Katie O'Byrnes.
Everything is accessible on foot. All of my visits were pre-Covid, so what's open now is anyone's guess. For a stay-over, I used the Stockade Inn in the Stockade district. There's also Proctor's Hotel downtown, about 5 mins. from the station on foot. It's next door to the historic Proctor Theater.
there is a free trolley that they run to some interesting places, but I don't know of its current status, or of any of the places it went. I was supposed to have a meeting at the Rivers Casino last month, obviously that didn't happen. there is a visitors website, it may have some up to date info...