1. Actually use your vacation days
Apparently 40% of Americans don't use all their vacation time. Knowing that most Americans get about 5-10 vacation days per year in entry-level positions, that makes me want to cry. Using your vacation days lowers levels of stress, making for an overall happier life filled with new experiences - or even just a relaxing couple of days off.
So, please, use your vacation days. Not just to fulfill your aching desire to travel, but for your health and sanity.
2. Travel on holidays
From a budget traveler's perspective, traveling on a holiday would be "taboo" in most cases since the price of flights, hotels, etc. tend to spike during holiday times. However, a holiday off work is a precious day off, and, if used wisely, doesn't have to be too expensive.
3. Schedule vacation days around work holidays
Since many work holidays fall on Mondays or Fridays, you've already got a 3-day weekend. Build that 3-day weekend into your trip schedule to maximize your time. This allows you to use less vacation days for one trip...meaning you can put those toward another trip later in the year.
4. Go somewhere nearby for a weekend getaway
Road trip somewhere close. Maybe you're traveling west to the beaches or to a winery a few hours away. Maybe you live close to New York and can just hop on a bus to get there. Maybe you live in Europe and a few hours on a train will show you to a new country.