what is the best way to get from hotel to theme parks?
if you are staying on Disney property their bus and boat system is free and awesome.
The fastest way has got to be by car. Still, if you're staying at a Disney hotel you could consider using its complimentary bus shuttles. The same goes for Universal Orlando's hotels. The Universal's Cabana Bay Beach Resortis a very affordable one.
Some neighboring hotels of Disney also offer transportation.
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Best way or the most affordable?
Best (most expensive, but still quite affordable if you have more than 4 ppl) -private car. We use STAR TRANS-VIP - http://www.startransvip.com
Cheapest-hotel shuttle to parks or any shared shuttle.
You can rent a car, but you will have to pay for parking.
Taxi? I do not use services like Uber... so I would recommend a yellow cab (ask for the number at the front desk).
Drive, or see if your hotel has transportation. Just check out the road maps ahead of time. Orlando is tricky and I-4 is currently under construction so its a disaster.
Most hotels have a shuttle, but it really boils down to how often and quick the shuttles are. ALL on-property Disney hotels offer complimentary transportation or are walking distance to theme parks. Transportation could be monorail, bus, or boat. The transportation runs very frequently and is generally convenient.
Most off-site, hotels offer bus/shuttle service. Some offer service a few times a day (once in morning, afternoon, and evening), some once per hour, etc. It depends on the hotel and the proximity to the parks.
Alternatively, you can take a taxi or something like Uber. These can be quite convenient, but can get pricey depending on the distance you need to travel and the frequency you need to use.
Then you finally can rent a car. Even when staying on Disney property I rent a car. It's not always the mode I take, but many times it can be convenient if you don't want wait for a bus to take you back to your hotel. (Although you might be parked in a giant parking lot).
Many of the hotels have their own shuttles to get you from their hotel to the Disney or other Theam Parks. Some are free and some will cost. You can also take a taxi. If you are staying at a Disney hotel they will have free shuttles or parking at all of the Disney Parks. Everything is very close.
Mears transportation is also an option if your hotel does not offer shuttle service.