Letchworth is okay, but it's not in Rochester. It's pretty-ish especially in the fall. September should be okay.
If you want to see stuff close to Rochester without too much of a hike out of town you'l have:
The Eastman House - Yes.
Hamlin Beach (State Park) - Meh, I grew up in Hamlin so it isn't that great to me, but it is definitely one of the better beaches in the area.
Rochester Museum & Science Center - Yes.
Strasenburgh Planetarium - Yes.
Seabreeze (Amusement Park) - No... It is overrun with trash and not a good park anymore. Sadly, once the buses started stopping there, the place took a turn for the worse. They didn't even open on Memorial Day this year because of fights in the past
There's several nice golf courses in Rochester if you're into golf (Oak Hill Country Club is notable) - Golfing is good, but I don't think Oak Hill is open to the public. There are plenty of courses around though.
Tons of fishing - Definitely. One of the main things I do in the summer around here, but unless you know someone with a boat you'll probably be stuck fishing from shore.
Eastman Park - If you mean Durand Eastman Park, yes. Awesome trails and views, plenty of wildlife to see. My dog sometimes gets ticks on these trails though, just a forewarning. The golf course isn't bad either.
Canal Park - Eh, its just another park to me. The bike path on the canal is nice though.
Speaking of the Canal - I don't know if they still do canal boat tours or not (The Erie Canal that is... it's kinda cool) - Pretty sure they still have boat tours, that could be fun.
Wegman's was mention - it's a grocery store, but I make abso-fucking-lutely sure to get myself a sub whenever I make it up there. - Can't beat Wegmans.
Speaking of subs - not sure if Dibella's is still kicking, but they're what Wegman's subs are inspired from. - Don't eat subs, and didn't even know DiBella's was only in this area.
The Garbage Plate was mentioned - that's Nick Tahoes. - I don't eat them, but whenever friends come back from being away for a while they always want one.
Shopping - there's tons of it, nothing notable. But the Mall at Greece Ridge was pretty huge when I used to live up there. I preferred Marketplace in Henrietta though, and there's Eastview Mall on the other side of the city in Victor. - Eastview is the only decent mall nowadays. Greece went to shit a while ago, and Marketplace followed soon after. They did some renovations at Greece Ridge, but it didn't help.
Unfortunately, September means you'll be between both the Red Wings (AAA baseball, just ends) and Amerks (AHL hockey, hasn't started yet) seasons.
That's some of the stuff to do in Rochester itself.
If you're willing to venture out of the greater Rochester area and drive within a couple hours in any given direction, then yes, you've got:
Letchworth State Park - Love visiting Letchworth.
Niagara Falls - Not really fond of Niagara Falls, unless I'm going to gamble. The US side is pretty run-down.
Catch a Buffalo Bills (Football) game - Tailgating is fun.
Hit the Finger Lakes Wine Trail - Definitely.
Syracuse (Basketball?) - Meh.
Darien Lake (Big Amusement Park) - I haven't been to the actual park in a long time, but go a couple times every summer for the concerts. See if there is anything worthwhile playing while you're in town.
Visit the Attica Prison and make a new friend - All my good friends live in Attica.
Go visit DrPizza and meet his goats - I'm not even sure where he lives, but I know it's south of here.