I live and work in the Galleria area, so I don’t know downtown like the back of my hand...but I’ll give you what advice I can.
If you show up early, you can probably find some street parking a few blocks away. Metered parking is around a buck an hour, depending on the area of downtown, and no charge after 6 pm.
If you get there a little later and can’t find any street parking, try the garage on the west corner of Lamar & Smith; I usually have pretty good luck there. Then it’s just a 5-block walk to Jones Plaza. And if you bring your appetite, there’s a Pappa’s BBQ on the same block as that parking garage.
Let me know if you have any other questions!
Parked in the II Shell Plaza gargage for 16.50. wow.