Three organizations - AARP, The Scan Foundation and the Commonwealth Fund have created "long-term care scorecard" that compares long-term care in all 50 states and Washington D.C. The report can be found at http://www.longtermscorecard.org/ . According to the report, the best state for providing long-term care is Minnesota and worst is Mississippi.
The scorecard uses a variety of indicators and methodology. For example, one is based on the percentage of 40 year old's who own private long-term care insurance. Here is a Bar Chart showing the states that have the highest penetration. Not surprisingly, there is a correlation between Long-term care market penetration and the ranking of the states.
Of course, the data doesn't show what typeof long-term care policy someone has - the biggest state by percentage of ownership by far is Maine, with 30% of 40 year old's owning a policy. This might be due to the fact that it is the headquarters of Unum, a large writer of worksite long-term care insurance that tends to market to younger audiences with modest benefits.