Check the Weather
Warm is good, hot is not. You will have a hard time spending 5+ hours in direct sunlight if it's over 90 degrees. The weather also helps indicate the depth of the water, which you should also check since kayaking in shallow water is a lot more of "using the paddle to push yourself off of rocks" than actual floating.
Pick a Place
As someone who went from casual drifting to Class II rapids, I can personally confirm that the river is not all one level. If you're bringing kids or looking for an easy float, check out a map or call a kayaking company to make sure that you won't have any heavy waves, drop-offs, or rushing water. It's exciting and epic... until "someone" has to bail water out of their kayak using a Tupperware container.
Pick A Good Company
Some pick you up when you call, some have scheduled pickups on the hour, some give rides in rickety buses while others have nice vans. The river is much less crowded on weekdays, but some companies will be overcrowded and stretched thin regardless of the day. Some businesses provide snacks or meals on the river. Figure out what you want, if you have any preferences, and do some light research.
Pick GOOD Company
If you're looking for a down to earth adventure, make sure you choose to go with a quality human being. Someone you can have awesome conversations with, or sit in a comfortable silence for a really long time with. Also someone who will voluntarily take awesome photos of you, and encourage you to step, or paddle, out of your comfort zone.
Wear Sunscreen, Drink Water
I may or may not have sunburned most of my body...
Enjoy every moment! If you're hot or feeling tired or stiff, hop out! Just make sure to pull your kayak out of the water. I pulled over when I saw a rope tied to a tree, and that ended up being super fun. I also stopped to see a group of cows walking through the water because I have a strong, and inexplainable, urge to get closer to friendly giants.
Do not be that one woman I passed who was yelling for her kids to jump in and look for her $300 sunglasses. No one likes that girl. No one jumped in. Waterproof your camera, use a life proof or ziplock bag for your phone, preferably bring a waterproof bag. If you're not willing to lose it, don't risk it. Here's a great guide for your packing necessities on a day trip.
Happy Adventuring! Let me know how it goes!