If your drivers license is suspended in one state, you generally can't just pick up and go to a different state and get your license. The reason you may not do this is because of the Interstate Drivers License Compact. This is an agreement by which 45 of the 50 states share information on things like suspended drivers licenses, DUIS, traffic convictions and other related matters. If your drivers license has been suspended and your state participates in this Interstate Compact, then you will not be able to get a new drivers license in any other participating state since they will have a record of exactly what is going on with your license and will be able to see what you are trying to do.
There are, however, some non participating states. These include Wisconsin, Tennessee, Georgia, Massachusetts, and Michigan. If you move to one of these states, they may not have a record of your suspended license and thus may issue you a license unknowingly. However, this doesn't necessarily mean you will be home free and able to start driving. You will need to get car insurance, of course, as you do in all states, if you want to drive. When you attempt to get car insurance, there is a very strong chance that your insurer is going to notice that you have a suspended license and they will of course refuse to issue you insurance on the basis of that.
Instead of trying to get a license in a different state when your license is suspended, the best thing to do is deal with your suspension head on. Contact a lawyer as soon as possible to get assistance in dealing with whatever caused your license to be suspended so you can move on with your life.