I can confirm that you can use you GA to go up to Rigi on the cog railway (for no extra charge) as I did this last weekend (this is something that I think the SBB recently changed). I also really recommend it for photography up there - I loved the view.

If you looking to make a day trip of it you might want to try the following:
Zurich - Arth Goldau, then up the mountain railway to the top. You could then come down part way on a sledge (rentable from the top for 10CHF + 10CHF deposit) and catch the cog railway the rest of the way down to Arth Goldau. Alternatively, use an different cog railway from the top to go to Viznau then Luzern - Zurich on the way back.

With weather - check out the Rigi mountain web cam before travelling. Weather was terrible in Zurich but great above the cloud in Rigi (could of course work the other way!) but good to know to check in case you are thinking of not bothering to go due to poor weather. Enjoy your trip.

As an aside for others if you do not have a GA card and have to purchase a rail ticket then this will be valid to travel as much as you want up and down on the cog railway and will also include a 10CHF voucher for the renting things at the top of the mountain (making sledging effectively free if thats your thing!).

Perhaps interlaken and the surrounding mountains might be an alternative for photos - although I am not sure whether the mountain railways there are free or not with the GA - check in your local station. You could then use your GA on the golden pass line route between Interlaken and Luzern which also offers nice views, obviously better getting off to take photos will work better - you could try Breinz and its lake for that (early morning was pretty nice lighting for me).

I reckon you could try some sort of combination of both trips if you were really keen and got up early enough. Early morning and later in the day are better for photography though right and you want the best shots