Not sure if it's combinable with the free day coupon (at least if you only park for one day!), but three visits to a Thrifty parking location earns you 250 bonus miles in many airline programs:
http://www.thrifty.com/specials/4208.aspx
Also, the link posted by
marisky23 indicates that three parking visits nets you 5 Blue Chip Reward credits. 16 credits gets you a free rental day, which can be a great deal if you're going to be renting during peak season somewhere--for example, that free rental day could be worth about $90 in ANC during the summer, which makes each of your parking visits worth almost $10 in rewards. (According to my math, that's three times better than the effective redemption rate of the 250 miles you'd earn if you figured their worth on spending 25,000 miles for a $1,000 domestic ticket!)