Where are you coming from?

Here are some ideas: Argentina, Central America, Greece, Thailand, Vietnam.

I should add that these places are all 'fairly' cheap, but very different, so it really depends on what kind of stuff you like to do. ie. do you want big city, beaches or more off the beaten path? or a combination?

I have just come back from a solo trip on the Hurtigruten in Norway.
It was my first solo trip since I married 36 years ago. I loved it - wonderful scenery, a few excursions to interesting places, relaxed atmosphere on board with a good mix of nationalities and ages. Food was good too. I never felt lonely, but also had plenty of time to enjoy being alone. In April you will have longer hours of daylight, but may still be able to go dog sledding or on a snowmobile trip for instance. You could also still experience the aurora - one of the highlights (pardon the pun) of my trip.
www.hurtigruten.com.

Singapore
Japan
Brazil
Bali
Butan

Prague
Costa Rica
Italy (Rome, Florence, Milan, Venice)
Barcelona

www.nuhousehotels.com Quito Ecuador

www.guanguiltagua.com amazing culture beauty variety.

Most varibaly Eco Dense country in the world for me

www.insuremytrip.com wise can get politically frisky there.

www.bolivar2.com Cuenca best climate in the world.

Also perhaps www.visitmorocco.com nice in April Arabian flair.

www.riaddor.com Meknes awesome there a little more expensive

to get too...

Have you checked out this thread for some solo information and inspiration? http://www.fodors.com/community/travel-tips-trip-ideas/goin-solonothing-like-it-a-trip-report-collection.cfm

I travel solo all the time, but unfortunately not in April; the type of weather you prefer to travel in can have some bearing on your choices, too, but I'm thinking maybe somewhere in Southeast Asia would fit your criteria and budget.

I would recommend Singapore. With such a rich multicultural heritage, it is no wonder that the variety of cuisines, restaurants, cafes and eateries has expanded.

I would highly recommend Greece—several days in Athens and then some island hopping. People there are so wonderfully friendly, which is always helpful when you are solo, and there isn't too much of a language barrier in Athens or other tourist areas. However, I believe that a lot of things in Greece shut down over Easter, so that's something to consider, depending on when in April you are traveling.