We're thinking of a trip to Yosemite for my wife's 60th birthday. However, I know absolutely nothing about the place, and it's pretty confusing trying to figure out where we wanna stay, and where would be the best place to try and camp?? I found a few campgrounds outside of the park, but again, I kn ow where nothing is up there.

We'd be towing our trailer, and want to stay 4 or 5 days. Here's what I've got so far:

35 foot travel trailer (is staying inside the park even an option??)

We want to hike up and see half dome, that's the main priority right now.

We'd like to stay close to the park, if we can't stay inside.

Which entrance would be best to stay near??

I'm sure I'll have more questions once you guys answer these!!

It is a crowded place with terrible parking.

I've only climbed there and camped in tents so I can't give much info on travel trailers. I'm not sure if it's too late to make reservations.
https://www.nps.gov/yose/planyourvisit/camping.htm

Half dome is a long walk, 16 miles round trip with a good bit of elevation gain (5000' elevation gain i think). You need reservations to walk to the top (cable section).

https://www.nps.gov/yose/planyourvisit/halfdome.htm