Like mentioned above it all depends on what YOU are looking for. Some 60-70 years old like to cruise with a mixed age crowd, while others like to try and cruise with mostly older adults like themselves.
More than just a specific cruise line, cruising options like cruise itinerary, cruise length and time of the year will greatly affect the overall demographics on a cruise.
You will typically find the younger average cruising ages on: Caribbean cruises, shorter cruises, cruises during school breaks (including summer)
You will typically find the older average cruising ages on: Alaskan cruises, European River cruises, American River cruises, World cruises, longer cruises
Take a 3 day Caribbean cruise over spring break: average age may be 28 years old.
Take a 8 day Caribbean cruise a couple weeks later on the same ship: average age may be 48 years old.
Those are just some generalizations that aren't always true, but for the most part they should at least give you an idea of what can be expected and what other options to look at.
Whatever cruise you take there will be others your age to interact with.
My wife and I fall into this age bracket. We did our first cruise in 2009 and this past February we were on our 7th one. Six were on Royal Caribbean and one was with Holland America. All were in the Caribbean. All were during winter months and not during school break. We found the crowd to be mixed and have made many new friends, most in our age bracket. We like to sit at a table of 6-8 people in the main dining room finding that a good way to meet new friends.
We will be cruising again in January 2015, this time doing 2 back to back weeks, again with Royal Caribbean.
We were 71 when we took a Carnival repositioning cruise from New York City to Long Beach, CA aboard the Carnival Miracle. It was a 15 day cruise thru the Panama Canal. I would say the average age was 50+. A lot of canes and walkers on board. It was a pleasant no noise cruise with very few kids on board. Other Carnival cruises we have been on had kids running down passage ways, hallways, and a lot of screaming. Kids will be kids but we will never take another cruise in April or during the summer.