Convincing your parents to move may not work if they do not have the desire to do so, but there are many ways to present a strong case. Identify your parents' personal, financial, health and social needs, and determine whether a new location can meet those needs better than the current location.
Deciding on the best ways to convince your parents to move depends on both their age and yours. If you are still living at home, and your parents are still working, their careers are probably one of the main reasons why they don't wish to relocate. Research the location where you wish them to move, then present your parents with viable job opportunities there. If one or both is interested in changing careers, a move can be the perfect opportunity.
Cost is also a major factor in deciding to move. If the cost of living is much lower in the location to which you want them to move, your case is immediately stronger. Affordable housing and a shorter commute is likely to appeal to them. If the cost of living in the new city is actually higher, be prepared to illustrate why it's worth the change. When a larger city is more expensive, it's often because of access to health and career resources, culture and amenities.
Whether you are a college student or independent adult, you may simply want your parents closer to you for personal reasons. Tell them about your need to have them in your life and the lives of your own children. Remind them that they are not a burden, and that you want to be there for them through any health and financial issues that may arise as they enter old age.