Retirement benefits allow you to retire and live off of your savings as you get older. You may not want to work forever, or you may not be able to work forever. Regardless of the reason, your retirement benefits allow you to relax or engage in a hobby that you've always wanted to pursue. The state in which you live could indirectly affect your benefits, particularly if you move.
Your state may tax certain retirement benefits at the state level. Some states exempt certain retirement benefits. Your choice of retirement and where to live may ultimately determine what you receive. However, your gross benefit before taxes, should not change regardless of where you live. These benefits are either defined benefit payments or defined contribution payments. Defined benefit payments promise you a specific benefit no matter what. Defined contribution plans do not promise a specific benefit, but also do not change if you move somewhere.
Your benefits are not determined by your location, which means you can live anywhere you want when you retire. Of course, you want to choose a location that is tax friendly. A low tax rate environment means you keep more of your retirement income.
The only disadvantage of moving from state to state is if you move to a state in which the tax base is high. If you move to a state that taxes retirement benefits, and you moved from a state that did not tax them, you are economically in a worse position, all other factors being equal.
You should pay attention to other taxes and the general cost of living in addition to your net retirement benefit payments. Some places are obviously more expensive to live. However, if your new home state applies a larger sales tax or use tax, or assesses larger property taxes than your former home state, you may receive more retirement income, but have less money to spend.