"Complimentary" shuttles will not cost you outright money (except for any voluntary tip). But they do not run at your whim. They may run every half hour or every hour or not so dependably, to the point where if it takes you 25 minutes to walk that 1 mile (if indeed it's an accurate distance*), it may save you time to walk than to wait around for the next shuttle to get there.

So it depends on how "special times" and how much extra time you can allow.

I know nothing about the specific shuttles for these specific hotels, but for example at many airport area hotels the shuttles regularly run to the airport (at certain hours, anyway), and if you're going somewhere else they may drop off the people at the airport first (even if your destination was closer) and then drop you off on the way back.

They tend to work fine for things like conventions where you if end up 30 minutes late it's not going to kill you.

Also, you have to factor in area traffic. A taxi may still give you unpredicatble travel times in heavily congested traffic areas (of which there are TONS in Southern California, sometimes at hours you'd never guess as a visitor), so if the timing of getting to the special place is very critical, you need to either allow extra time for traffic (and extra extra time for a multi-stop shuttle going through that traffic), which you wouldn't at a more expensive but closer hotel.

*Those distances should be either verified (at least with a map) or else taken with a grain of salt. Also, just because someplace is walking distance in the US doesn't NECESSARILY mean that it's walkable. Your hotel (especially in the suburbs) might be on a very busy highway where there's no sidewalk, no good place to cross the street safely, etc. And getting solid info about local walkability around a specific hotel can be a big challenge.

One place you should look to see if you can get more specific independent info about a hotel is www.tripadvisor.com -- it's the leading general site (not specific to frequent flyers ) where people post reviews about hotels they've stayed. In some cases those reviews describe the surrounding much better than any other sources I've found, if I can't find someone on FlyerTalk who's been at that hotel and paid attention to the surroundings. (Many FTers staying at suburban hotels in the US have a rental car or are just taking taxis as a matter of course, and might not notice how "walkable" the surrounding of the hotel are, if no one asked them that question BEFORE their stay.)