PURSE:
I usually carry a tiny backpack that holds my wallet, Elph camera, bottled water, and phone, just b/c I hate all that weighing down my pockets and I hate holding stuff on rides. It carries the minimal stuff I don't feel comfortable leaving in the stroller.
BACKPACK/COOLER AND OUTSIDE FOOD:
I have a backpack or cooler on my stroller, usually. It's filled with bottled water (try not to buy these in the park - $$$$$!) and some snacks for DD. If I remember, I throw some extra bottles in the freezer overnight. They do check all your bags & stroller compartment at a checkpoint between Downtown Disney and the entrance to both parks (DL & DCA), but I've never been stopped for having food. If they pushed, I'd just tell them that DD has a food allergy. (The official "rule" is outside food has to be consumed outside the park in the tiny picnic area right next to the Downtown Disney tram drop-off area. I have NEVER EVER seen them enforce this, though.) If it's an all-day adventure @ DL, I pack TONS of snacks for adults too.
The main bag/cooler stays with the stroller in stroller parking areas. I just refuse to pay for a locker and have to walk back to it all the time. I've never had a problem with theft or anyone pilfering thru my bag. We all paid big $$ to get into the park - people are usually in a rush to park the stroller & go themselves. If they're *that* desperate for water or snacks, they can feel free. I don't keep anything of value in/on the stroller anyway.
STROLLERS:
I put colorful duct tape on my stroller to differentiate mine from the others. There's also matching tape on my cooler. I've seen streamers on some but I think that gets in the way when you fold it to ride the tram.
TRAM:
The stroller car (usually the 1st car on the tram) is the longest wait b/c people don't fold up their strollers and it fills up quickly. To save time, empty out your stroller while you're waiting, fold it up, and get on a regular bench. You can usually get on the next tram that way. I just put the stroller next to me or on my lap. Personally, I don't think the time wasted waiting for a tram (keep in mind you'll be waiting all day) is worth me not having to fold it up.
JACKET/PARADE WAITING:
Don't forget a jacket. Or layer clothing. DL gets cool at night and you may not want to spend $40 for a kids' sweatshirt that's not all that warm. I usually also throw in a blanket or towel in the stroller storage. I have a wet/dry one that I can also use to reserve space & sit on during parades. I usually line up for parades an hour before they start. I park the stroller and spread out the blanket only for the space I need/use. A NeatSheet/throwaway tarp would also be good for this use, but can't double as a blanket if your DC gets cold. I'll usually go wait while DH is taking DD on rides to cut her waiting time.
FINDING NEMO:
The Finding Nemo ride is really cool. I noticed it is less crowded during parade times (check 30 minutes before as people are waiting for parades) and the line is more bearable when it's darker. It's an underwater ride so it's not going to make a difference whether you ride it during the day or night, IMO. I've done both. I'm willing to wait in line if it's not curled up around the lagoon. It's about 45 minutes from the point where the line starts spiraling (right after the exiting line crosses the wait line). Keep your stroller in line with you so your DC can wait in it. A cast member will take & park your stroller for you when you get to the 15-minutes-from-here sign.
FASTPASS:
We usually get a FastPass right before we eat. Usually it's from Autopia or Buzz LightYear. Those lines aren't very long anyway and the FastPass wait is about 1-2 hrs. I wait for the FP time to come & pass; then I save it as a trump pass whenever we're doing some last-minute rides. Remember that not only can you use your FP any time after it "expires" for the night, you can also get another one from any other FP ride. We usually take the Monorail to/from Downtown Disney so Autopia or Buzz Lightyear are it for us on the way out.
ROGER RABBIT/TOONTOWN:
The Roger Rabbit FP is another one you can collect right as you enter Toontown. You can play, eat, tour Mickey & Minnie's house, and ride the roller coaster while you wait for your FP time. If you do the princess show, send someone to collect the Roger Rabbit FPs for you so you can kill time at the show. One caveat - the Roger Rabbit ride breaks down often, IME. Once your FP time comes up, if it's open, you should ride it if you're in the area. You don't want to walk all the way back to that end of the park only to find out the ride is broken.
PRINCESS FAIRE:
If you plan on doing the princess meet & greet, keep in mind the line is VERY slow. Ask a cast member to guesstimate wait time. Either I or DH will stand in that line while DD watches the show or rides on Its A Small World (which I think is closed now). When I'm about 15-20 minutes from the front, I'll have them come back to the area and just color in the princess shoppe area or watch another show. Thank God for cell phones! The meet & greet is a great opportunity to get 3 or 4 princess pictures at once on a Disney PhotoPass, but it's the worst wait b/c it's so much idle standing with nothing to do or see.
BABYSWAP:
The BabySwap that PP mentioned is a really good idea. Not many people utilize that, but it's a way for your DC to ride 2x on rides like Dumbo (long line, short ride).
EARLY ENTRANCE:
I think the early entrance is for park/property guests - being a passholder, I never got that. If I was lucky enough to do that, I suspect I'd go right to Autopia. I seem to remember a post here about a couple people who got DreamFastPasses that way. (you could do a search to make sure) It's really a
[email protected] kind of thing, but hopefully if you're in that area, maybe the Finding Nemo line won't be too long...
ITINERARY:
If you're going on a weekday, it shouldn't be as crowded and you could probably ride a lot of rides. I wouldn't stress out about an itinerary - as long as you get on the ones your DC likes, it'll be a good experience. You could plan ahead by knowing which ones you'll skip and also allowing times for parades if that's what you want. My DD isn't that into Pooh anymore so I don't even go past New Orleans Square anymore. I'm glad she's finally outgrown it b/c we'd walk all that way past Splash Mountain only to ride that Pooh ride and watch the Bear Country show.
GRUB/RESTAURANTS:
Have you thought about where you want to eat? I vaguely remember a site online that lists the menus for all the DL restaurants. I'll try to find it. I tend to pick the ones with healthier kid options (not hot dogs or mac & cheese). If you plan early enough, you could make reservations/priority seating. I've never eaten at the Blue Bayou b/c I forget to plan ahead to make the reservation. The Plaza Inn is a fave and also the "Ratatouille" restaurant (the name eludes me now). I can also do the Tomorrowland restaurant. I hate the Bear Country restaurant and the Fantasyland one (something "haus") for kids meals. I'm also not so hot on the Toontown restaurant, either. Try to eat at off-times when the restaurants aren't so busy. I've found the worst time to eat is right after the night parade - wait times everywhere (even Downtown Disney) and that's when DD is the hungriest! Do try to eat before then.
Phew! That's all I can think of for now. If you have any more questions, feel free to ask!