In your OP you did not state how long you wish to be away.
However, I took two long term holidays (or vacations) when I was single.
The first one was to Israel for three months in 1994, which I spent a couple of months at a Christian conference centre in Isfiya, near Haifa. This was followed by a month at a backpacker's hostel in the Old City of Jerusalem after my contract at the conference centre ended.
The second trip was the better of the two. For ten weeks in 1997 I took off from London to Singapore, where I spent nearly a week. Then from there to Cairns, Australia, spending six weeks to bus down to Sydney. The highlight of this was discovering the Great Barrier Reef, first to Green Island from Cairns, then to Low Isles from Port Douglas, both while staying at a hostel in Cairns. Then I took a day trip to Whitsunday Islands, collecting me right at the hostel at Cannonvale, near Arlie Beach. This included snorkelling at the Fringe Reef at Heron Island. At Sydney, I bought a seat at the famous Opera House, to see a concert. After this I flew across the Pacific Ocean, over Hawaii, from Sydney to Los Angeles. I stayed in California for nearly a month, the best place was at a hostel in downtown San Diego.
Hostelling is the best way to travel on a shoestring budget. For lack of privacy - since you sleep in a dorm ranging from just two beds to about a dozen beds - you make many friends and exchange travel experiences. Each hostel has a kitchen, therefore buying groceries and cooking your own meals does wonders to the budget and gives a greater sense of independence and responsibility. Two good friends I made while hostelling were bricklayers, an Irish builder in Israel and an Aussie in San Diego. Both had short contracts which allowed them to earn a living while on their travels. For me,it is a life changing experience.