Like some others have said, I'd take a close look at the Disney Springs Hotels. Most of them should be well within your price range for late January/early February. Plus, they all offer 60 days FP+ booking (just like if you were staying at a Disney-owned resort) and Extra Magic Hours (though the benefit technically runs through December 2020, they always say that and then extend it; especially given the current situation, I don't see them taking away that benefit next year). They also offer free bus transportation "every 30 minutes." With the exception of the Swan and Dolphin, I think the DS Resorts offer the best, most reliable complimentary transportation to the parks of any offsite resorts. Keep in mind, it can take a while and it's far from perfect, so I think it's not a bad idea to still rent a car but you can always fall back on the bus if needed.
Perhaps the greatest benefit to the DS Hotels is of course their proximity to DS. I think the further resort (which is the DoubleTree) is about a 15 minute walk to DS but some hotels are as close as a 5 minute walk. While many think DS is a more adult-oriented destination, I think it can be wonderful for kids too! When you enter from the DS Hotels walkway, you're right near an awesome toy store called Once Upon a Toy. Nearby there's a wonderful
Lego Store and lots of family-friendly dining like T-REX and Rainforest Cafe (be warned, go here for the atmosphere/theming, not the food; there is way better food throughout DS). There's also a great candy store (Goofy's Candy Co.) there that I must admit I still love even as a fully-grown adult. Plus, if you're planning on dining at any of the WDW Resorts during your stay, you can just take the bus from the Bus Depot at DS rather than driving or transferring busses at one of the parks.
If you're looking for the DS Hotel with the most "Disney Moderate-equivilant" amenities, I'd probably point you toward the Hilton Buena Vista Palace. The pool area is fun and family-friendly and there's a great grab-and-go called Citrus 28 for a light and inexpensive bite on your way to the parks. The BVP is about a 5 to 10 minute walk to DS, depending on where in the hotel you are, and it's not unheard of to see nightly rates there in just the double digits during the slower times of the year (late January/early February being a slower time of year). You can also usually get a decent price if you're a
AAA member or check sites like the DISBoards and MouseSavers frequently. Both sites sometimes partner with the hotel to offer reduced rates. For example, MouseSavers is offering 10% off and free parking for BVP right now. Another great option for families, but further away from DS (about 15-20 minutes) is the DoubleTree with its spacious suites but the pool here leaves something to be desired. I also ike the B Resort but it's admittedly more of an adults hotel (though I've seen families there all time).A few DS hotels I'd avoid: the Best Western, the Wyndham properties, and the Hilton Lake Buena Vista (don't be fooled by its convince to DS, the hotel itself needs renovating).
Another option, ideal for someone with a car, would be the Hilton Bonnet Creek. While the bus service to parks from this resort leaves a lot to be decided, which doesn't really matter if you're driving, this hotel has A LOT to offer, especially for families. From an amazing pool complex (second in the Orlando area only to YC&BC in my opinion) to a plethora of well-executed onsite dining to access to some of the more upscale amenities next door at the Waldorf, I'm a big fan of HBC and the WA. They also enjoy EMH benefits (again technically through Dec. 2020 but I'd bet that'll be extended) and 60-Day FP+. Since the hotels started offering those benefits, I noticed the prices (especially for HBC) climb a bit, so it might be on the other side of your price range, but perhaps with a AAA discount, you could swing it.
Before she knew it, she could do the Cupid Shuffle!!! Afterwards we enjoyed one of the BEST drinks I had in my life, a "Banana Cabana Colada"!!! ....or two...or three. 
After the Coladas kicked in, I had to recruit my DD to help me teach her the "Cha-Cha Slide". Both dances are easy to learn because they tell you what to do in the song. To her surprise, she came there not knowing any line dances, and left knowing how to do two dances. And because she was good at it, she was no longer shy!!! My DH did catch that on video. This is what vacation is all about to me. Happy memories. I don't get how people can stay at places like this and not enjoy all the fun stuff timeshare resorts offers. I ALWAYS have a GREAT time!! I wanted to add a mini cruise to our trip in the near future. I know we will enjoy it, but we will STILL be looking forward to getting off the cruise and heading to a resort in Orlando/Kissimmee for 10 days!! 
Ridiculous!!! 
