omg, I wrote a book! Sorry so long. I guess I had a lot to tell you about!
I'm gonna answer your questions, then give you a BUNCH of advice that I wish I had known when we first went...
- We have a 2 yr old. Do we want to bring the stroller in, or just bring a backpack with all our stuff? I personally didn't like bringing a stroller. It slowed me down a lot, and I had to park it a lot too. In the end, we just walked it. the place is big, but there will also be many people to weave around. Not having a stroller makes you more mobile and more able to partake in museum displays, etc.
- Anything we should do first? go get your Planetarium tickets. If you go later in the day, they could be out (they are included with your admission). more about that below.
- Make sure we bring in our lunch or eat ahead of time. We always ate in the "sack lunch" area. I used to hang our coats and lunch bag there, so I didn't carry anything around but my purse. I'm not sure if it's still there. we've also eaten in the normal lunch area, off the food court. It's loud, and I always wiped the tables and chairs down before we sat. You can eat there... just bring your food into the lunch/eating area. Food that you buy there is overpriced and not that yummy.
General advice... Now, please remember that we had a membership to this museum for several years. We haven't been there in at least 1.5 years. I've only been a couple of times in the last 3 years. (DD is now 8). When I was a SAHM, this place was my lifesaver - I would take DD for a couple of hours at LEAST once a week. Here's what I've learned over the years...
You will be tempted to go to the playscape. From personal experience, do that last, or you won't see any other parts of the museum! Send one parent in first to see if it's something your child would be into, and think about how hard it will be to tear them away from the activities in there. My kid never wanted to leave the water table and the sand tables, and the giant wall puzzles.
Dinosphere - Enter the Dinosphere from the main entrance, near the food court. If you enter the other way (from the trains) you won't get to see the pterodactyls flying overhead or see the HUGE crocodile ancestor. Let your kids dig (past the dinosphere), but don't spend all day digging - there's so much more to do! Take a cute pic of kiddos in their goggles digging for fossils.
The dinosphere can be very scary for small kids, especially during the rain storm. It is a neat space though. there are little dinosaur costumes off to the side (to the left of the lab) that the kids LOVE to play in. There are also places in the displays for them to crawl under and pop up to take a closer look at the dino displays. Also check out the dinosphere from high up. (take the stairs up 2 or 3 floors. great views, especially during the storm, which takes place every 22 mins?
Be at the water clock before 1:00. It's a cool presentation/show. (water clock drains. I think it's 1. Maybe it's noon? I think 1 though. You can ask at the info desk - they'll tell you.
Get your tickets to the planetarium show right when you get there. If you go later in the day, the tickets may be all gone. (the programs are included in your admission - DD LOVED the sesame street one when she was 2... she's 8 now, I don't know if it's still there) Schedule here:
http://www.childrensmuseum.org/planetarium
The water play areas in Play scape (level 3) and science works (level 4) will be your nemesis. There are a LOT of kids who are being taken away from these areas - especially Playscape - thrown over their parents shoulders while kicking, screaming and crying because they don't want to leave. Bring dry clothes, just in case... we've seen many kids leave sopping wet.
SciencePort - level 4 - While the Science port may look like it's for big kids, there are littler kid activities further into the room. There are digging little excavator things (like on a playground) and there are foam pieces that look amazingly like rocks. DD LOVED shoveling them into a wheel-barrow. The underground ant hill thing - it can be scary inside. It's dark and cramped and one of the walls displayed the bones of a buried pet (with collar). Just an FYI if you don't want your kid to freak out. Some kids are fine with it. mine was NOT the first time. She was ok later times though.
basement -
The Chihuly area on the basement level under the chihuly exhibit - great place for the whole family to stop and take a rest. It's really relaxing and fun to lay on the rotating seat thing and gaze up at the beautiful glass sculptures. my fave is one that looks like a hurricane. See if you can find it! Your kiddo will enjoy sticking the "glass" pieces in the bases to make her own "sculpture"
Look up! there will be trains that go by overhead - it's so cute and fun to see them! There's also a place for your kiddo to crawl under and pop up "IN" the train display.
Story Avenue (back corner of level 3) is worthless. Don't waste your time. It's kinda creepy, but if you need a quiet place where there's no one else - you can go there.
That's all I can think of off the top of my head. Hope it helps and you have a GREAT time here in Indy. If you have time, check out our zoo too - it's a lot of fun!
Also, if there's a Indy Indians game on Sunday, the kids get to run the bases after the game, AND they get a free meal with admittance. It's a pretty good deal. (actually for only $15/kid, you can get a Knothole Club Membership, which would also get you a free shirt, and admittance to the game, which on Sunday would also get your kid a free meal - hot dog, chips, and a bottle of water).
If you need any more advice on Indy, you can PM me. I'm a local!!!!
Especially the tip about bringing extra clothes. MINE will be the girls that are sopping wet... 
