n a pinch, a variety of footwear will serve for faire-wear. Given normal length skirts, a pair of DocMartins are easily concealed, and very comfortable for a daytime of walking. Slightly better are closed-toe Birkenstocks or other natural leather shoes. Peasant men can conceal their footwear by wrapping their feet and calves with lashed down rags. This is to be much preferred over kung-fu slippers or other thin soled shoes: these will leave you sore.
Once you've made up your mind to buy specific shoes for faire, you'll find that there are two primary choices: low shoes and moccasins of varied height. To be historically accurate, you'd wear low shoes. As beautiful as tall boots are, the Cavalier style is better suited for mid 1600s Stuart period and in any case peasants wouldn't waste money covering their calves in leather! But for better or for worse, the moccasin look is an accepted norm and you won't win any friends pointing out the inaccuracy in their new $500 boots. For the shoe obsessed, take a look at A History of Shoe Fashion by Eunice Wilson.
For historically accurate 16th C low shoes, take a look at offerings from Pilgrim Shoes and Plantagenet Shoes. You can also modify off-the-shelf modern shoes into period correct shoes. Under your low shoes, you'll wear knitted hose or wool stockings (yes, even you men -- Elizabethans were very manly fops).
Moccasins are custom fitted to the wearer's foot, which means in addition to being acceptable faire footwear, they are VERY comfortable. While visually similar, the prices seem to vary dramatically depending on the maker. A base starting price is ~$250US. Good moccasins should last many many years, requiring only the occasional new sole (~$25). [My moc soles lasted for about 8 seasons of faire, I resoled them (Shraeder Bootworks below) and they're like new again. Ahhh.]
For the budget minded, the Minnetonka Moccasins can't be beat, but don't expect to get more than 10 or 20 hard weekends out of them: they're better suited to the occasional patron rather than the dedicated participant. I wore Minnetonkas for two years before investing in real boots and the difference is amazing. My feet NEVER hurt in the evening. I scoff at rocks.