There's two questinons here--Albany itself or out on the road on the former A&S.
Operations in and around Albany itself are pretty regular.
Best bet is to show up at Kenwood a little before 8 AM. The NS intermodal train (169) will be somewhere around, getting his train together for departure.
If you get there early, take a swing down through the Port of Albany on the main access road, you may see the Albany port RR switcher at work, or the remote-control switcher at Cargill across the street.
About 9:45 or so (check the timetable) the first passenger train from the west will roll down West Albany Hill and cross the D&H by the Central Warehouse. CSX often has a local to Troy or Rensselaer (depending on the day of the week) coming down the hill about the same time. Best bet is MWF to Troy, Tu-Th to Rensselaer.
514 -515 has been a wild card timewise, this is the CP's manifest freight, can show up any time. Lately, the southbound has been leaving his train outside the yad, with the back end extending up into the concrete canyon, then returning north.
168 (inbound NS inermodal) arrives mid to late afternoon and ties up.
The NYC train now originates at Kenwood, I've only seen him a few times, but seems to be an after dark departure this time of year.
There's a local that goes up to GE Silicones in Waterford (oops, make that Saudi Silicones, or whatever the new company is called). Often a mid day thing. Carries a caboose most days.
The Kenwood yard crew has some switching responsibilities at least as far north as Surpass chemical and the nearby team track. Both located on Erie St just south of the I90 overpass. Haven't seen him go out in ages, but used to be a late afternoon trip.
If things get slow, there's always something going on at Rensselaer across the river.
If you want to go out on the A&S as indicated in your title, that's best done on a different day than the Albany area itself. One good strategy on the A&S is to go to Esperance Station (south end of the Delanson passing siding, located where NY route 30 ducks under the main line) early in the morning. Real common for there to be a meet there in the first few hours of the day. Chasing from there south is a snap--just follow NY route 7 and follow your nose. Use I88 if you get too far behind.
The next siding south is at the summit of Richmondville, sandwiched between I 88 and NY route 7. I normally try to avoid using the interstate between Worcester and Richmondville, a long run between exits if you get surprised by a train. But the flip side is that you can readily read the southbound signal at CPF 528 from the interstate and get an indication of whether a meet is being set up. And truth be told, it isn't all that risky to pull an (illegal) U turn on that remote section of I88.
168 and 169 are pretty dependable mid-day trains, if you can overcome the revulsion of seeing NS power all the time. CP stuff a good bit less predictable, but in general mornings are better than afternoons for traffic.
Good luck!