Notice the qualifier. If your characters are using a synonym for look every other paragraph, you’re going to sound like you swallowed a thesaurus. Characters need to do other things, too, and there are other senses besides sight. And all of these words are more noticeable than look, so if you overuse them, it will be painfully obvious. If a character ogles someone on every single page, people might close your book in sheer embarrassment.
The original list I took these from, on Scott Myers’s blog, had ninety synonyms, and some of them were rather obscure, so I whittled them down to half for you.
My list: glance, regard, behold, review, cast around, scan, catch, inspect, scope, check, watch, scout, scrutinize, see, double take, mark, feast one’s eyes, eyes, eyeballs, note, spy, notice, spot, observe, squint, flick a glance (although I’ve been told only women do this), ogle, stare, focus, once-over, study, gander, overlook, survey, gape, peek, gawk, peep, gaze, pore over, view, glimpse, watch, witness.
Some possibilities: stroll, saunter, amble, trudge, plod, dawdle, hike, tramp, tromp, slog, stomp, trek, march, stride, troop, glide, wander, patrol, ramble, tread, prowl, traipse, roam, mosey, step, stride, steer, shepherd, accompany, scamper, scuttle, meander, sidle, and (in the right context) crawl, run, jog.
I hope these help. Happy writing.