I have some particularly "comfortable" squirerels nesting in a tree in my backyard. They dig up tulip bulbs, chew up my kids' toys, drag out the garbage and strew it everywhere.

My kids want to put in a vegetable garden. What are plants/veggies that squirrels do NOT like? And what ore other effective methods to keeping them out of the beds? Caging each plant is not realistic. Does this mean I can't keep the squirrels out?

There are no vegetables that are truly squirrel-proof. There are various methods to try and keep them at bay but it varies considerably and all of the methods will not work entirely all of the time. Your best bet is to try and contain the garden with netting or fencing. This would work if you plan to have a small garden. They tend to mess with plants in smaller stages, so keeping them way from new plants and seedlings is important. That's where objects that make noise- pie pans, pinwheels etc. help. While it may seem counterproductive, feeding them in another location well away from the garden can distract them. Also, scents such as peppermint, garlic, pepper sprays can be used as repellants but need to be reapplied after a rain. You might consider planting small gardens in patio containers, where you might be better able to manage the situation. There's no easy solution to a squirrel problem.