Myrtle Beach is flat & walker friendly. It also can be warm & humid. If you NEED to do the 50 state thing (I'm doing it too) then you should consider what it will cost to run/walk vs. what it would cost to reschedule the whole thing. As long as you can live with a sucky time, you can get through it. Be sure to take it easy so you don't injure yourself. I would do the run/walk thing right from the start. Try it on your 'long run' this weekend. If you can do it for 10 miles or so without it driving you crazy then it might work for you. Some people hate it.
Once I started working towards the 50 state thing I found it helped me recover faster. The first time I used it I was coming off an injury and HAD to do a local inaugural marathon. I did a 4:1 run:walk and walked through the water stations. It gets the job done, not pretty, just a completion. Post back to tell us how it worked out.