Answer
There are 256 travel options.
Work Step by Step
The set of cities is:
{New York City, Los Angeles, Miami, Chicago, Washington D.C., Houston, San Diego, Seattle}
The number of ways to visit some, all, or none of these cities is equal to the number of subsets of the given set.
A set of $n$ elements has $2^n$ subsets; therefore, the given set has:
$2^8=256$ subsets.
There are 256 travel options.
