Yes you can purchase a home anywhere you want. Since my husband is a retired teacher & I was a realtor, I know first hand that 90% of realtors are stupid and don't understand that retirees CAN qualify for mortgage loans OR pay for their new home with cash.
Lenders do understand that retirees income is either pension, Social Security and/or investments and savings. All of these sources of income counts towards buying a home but all realtors think of as income is a job. Therefore, to get past the ignorant agents, you will need to have a pre approval from a lender OR a statement from your financial institution if you are paying cash for your new home.
Final tip: Don't let realtors tell you what type of home may be more suitable for you. Stick to what you are qualified for. Agents are goood at twisting the truth to benefit them.