I do get pain on the bottoms of my feet (along with the rest of my feet, yay, fibro). I am told by my massage therapist that I likely have plantar fasciitis. I've been working really hard on getting the knots out by standing on a hard rubber ball and rolling it under my foot.
I also have neuropathy-type pain when I first get up. It really hurts when I stand up for the first time in the morning. It does generally wear off after I've been up for awhile.
Maybe sitting with your legs crossed is aggravating a nerve or something? I can't cross my legs anymore because it makes my feet go to sleep. I have rather crummy circulation.
Make sure you bring some cushioned, well broken in shoes with you on your trip. Nike walking shoes (tennis shoes made for walking) work best for me.
Good luck to you.
fanfaire