Probably best to check the website for any local hotels you are considering. Prices fluctuate based on the season as mentioned above. Charging a 'resort fee' is now a common practice with many hotels.
I see the resort fee on the Expedia website. It’s under policies. The “additional inclusions” include parking according to the hotel website. So there isn’t a separate fee for parking since it is included in the resort fee.
I don’t envy you the task of finding a no fee property. I try to avoid those fees whenever possible myself, as I see them as nothing more than a money grab. If you are going to check properties on a site like Expedia I recommend looking at the policies page for fee information.
If you have a car the Fairfield Inn Lake Buena Vista in Marriott Village is under $112 a night. That is with a $20 charge and 4 nights of parking at $25 each.
The hotel has breakfast and apparently a shuttle.
Never stayed here but it looks like it would be close to your budget.
One year our flight got cancelled, Disney was sold out and we had to scramble to find something and stayed at Rosen Shingle Creek (I would not stay here again) and it looks like they still charge for parking.
We stayed one night at Hyatt House Orlando / International Drive. I believe it has no resort fee, but we booked on points so double check that. Free breakfast and free parking. I took a look and your dates are $102/night before taxes.