They are doing construction (think it is new apartments) right next to Residence Inn but I believe the sidewalk in front is still open. If it is you can turn left as you leave RI, walk to the light, cross Westwood Blvd, go to the next light at Central Florida Parkway and Sea Harbor Drive, cross over both streets (there are crosswalks in all directions) and then walk down Sea Harbor until you reach the parking lot exit, then just cross the parking lot. It is sidewalk all the way and you have walk signs and cross walks at the intersections. I have walked it many times and it is completely safe since you are on sidewalks the entire time.
If for some reason the sidewalk in front of the construction is closed you would have to cross Westwood on your own (or just walk on the side of the street past construction). There are also sidewalks on the other side of Westwood, so once you do cross you can use the sidewalk the entire way again. The only difference is that Sea Harbor meets up with Westwood along there, so you could actually take Sea Harbor from there (the way it curves I believe the actual distance would be shorter) and again it is sidewalk all the way.
Sorry - never actually stayed at RI so no tips there, just walked by it many times.