Hello! So I'm flying back to the states from Australia and land Monday morning in LA. I'm thinking of rebooking my flights to bring me back to Orlando on Tuesday and spending Monday at DLR. Few quick questions.
I haven't been to
Disneyland in years. Any can't miss things if I do end up going?
There's a lot that I would consider 'can't miss' but if you're doing just one day and with it being President's day holiday it will be busier then normal (I'll be there with the family this weekend too fighting the crowds) and it may be harder to get everything in. On the other hand since you'll be solo it will be MUCH easier to get around and take advantage of single rider lines where available. I would definitely recommend a park hopper. I always find Disneyland to get much more busier later in the day and it can be slightly less crazy over in California Adventure. Once the crowds get unwieldy in DLR you might get some breathing room in DCA. But some of the top few things not to miss right now:
Seasons of the Force overlay in Tomorrowland
Hyperspace Mountain
Star Tours
Paint the night parade
Disneyland Forever fireworks
Churros
In DCA Check out Cars Land and do on Radiator Springs Racers (single rider line available)
I always recommend taking a break at the Carthay Circle Lounge. A great quiet and cool place to grab a snack and adult beverage.
Also a heads up the weather right now is calling for temps to get up to 95 on presidents day! Bring sunscreen and a hat

Even a better reason to take a break in the Carthay lounge for an adult beverage or 2.
Use the Disneyland app to plan what else you want to do, you can see current wait times and gives you a park map including your current location.
Be sure to look at the Disneyland calendar. I'm going there with my family this weekend through some of next week and saw there are quite a few scheduled refurbishments going on:
President's Day Calendar
Is there transportation to/from Disney resorts to LAX?
Never had to use it but as
@theluckyrabbit mentioned lookup the Disneyland Express
Would it be better to stay at a Disney hotel or one right next to Disneyland?
All depends on budget but I would say for as little time as you'll be there I wouldn't pick a DLR resort hotel. If you were going to the park the next day you would get early magic hour entry into Disneyland. But if you haven't already looked I would expect prices to be $400 or more for 1 night at one of the resort properties. Since you likely wouldn't be spending much time there I would opt for a hotel there on harbor blvd. Many of those are just as close to the gates as the DLR hotels. I've stayed at the carousel inn which is very close and reasonably priced. I've also stayed at the Doubletree but it's a bit of a walk, about 15-20 minutes to the park. There are plenty of other good choices right there.