We just stayed at the Hyatt Place on Caravan Court at the beginning of April and it was easier to walk over then to drive our rental car ($10 parking). It took longer to go round and round the parking garage then it took to actually walk over.
You just walk up the road to the light. Cross over at the light (major highway) and then there is a pathway to take you right to City Walk. It was very easy. We saw many people doing this regularly. My 13, 11 and 6 year old walked both to and from each day. My 6 year old enjoyed counting the little alligators (as he called them) along the sidewalk. We got to about 40 at one point.
They have a shuttle and it ran something like 8:20am, 10:30am and 11:30am. Then, it would come back twice about one and two hours before the park closed. So, even if you walked one way and took the shuttle back, it wasn't bad. The shuttle going was more convenient than the one coming back due to the times. One time, my husband headed back to the hotel a little earlier and when we were ready to leave, he swung by and picked us up at the Valet line which was empty and took up back to the hotel.
The other nice thing about The Hyatt Place was they had a Cracker Barrel across the parking lot where we walked to and ate almost every night and stocked up on candy for the parks the next day. Also, across the other part of the parking lot was a TGI Fridays. One night after the parks, we walked by TGI and my husband stopped in while we continued on to our hotel. He went in and got a bunch of appetizers to go and brought them back to the room while we watched the Final Four game.
And, the staff at The Hyatt Place was unbelieveable!! So, so nice. Anything we asked for, they ran for it and with a smile on their faces.