Yes here are three hotels that I would recommend.

The Red Roof Inn on Hampton Avenue
(314) 645-0101
(314) 645-0119
5823 Wilson Avenue
St Louis, MO 63110
It's cheap and clean, my parents stay there when they are in town.

Holiday Inn Express St Louis
(314) 664-0953
(314) 664-3596
(314) 773-6500
2625 Lafayette Ave
St Louis, MO 63104
This is very nice but will be more expensive than the Red Roof Inn, but probably not too bad.

Hampton Inn
(314) 241-3200
(314) 241-9351
2211 Market St
St Louis, MO 63103
This one is downtown and probably a good choice if you plan to do some site seeing while you are here.

And yes I would rent a car. Cabs can be fairly expensive (pretty much like anywhere else) $40 from the air port, and average $10 or more for short trips around town.

Things you might want to stick around and see are:

The Arch (of course)
The City Museum
The Anheuser Busch Brewery Tour (kid friendly!)
The St. Louis Zoo (free!)

And any number of attractions and museums here--if you plan for them outside of Vloggercue.

Bill Streeter
LO-FI SAINT LOUIS
www.lofistl.com