If you’re going to the Tower, I’d just stay in that area all day, there’s so much to do.
The Shard is a quick wander up&across the river from the poppies, and you could do the Monument on the way, tall buildings old and new 🙂
If you like gallery mooching, the new Tracy Emin is on at the White Cube in Bermondsey (free), which is about ten minutes wander from the Shard. The Design Museum is close by, too.
Maltby St/Spa Terminus is a good call for munching, only in full swing on Saturday though I think? Worth grabbing a coffee from Monmouth on your way past Borough Market if the queue’s not too long…
I lived here for years and still love the standard South Bank wander of Globe, Tate Modern, BFI, Southbank Centre then a gawp at Big Ben. Then walk into Soho and get some dinner (&Princi for dessert, nom).