You can get a cultural experience on both islands, Grenada is less developed and a really beautiful friendly island, Barbados is not touristy at all on the east coast but in general is more developed. Again you can have budget friendly accommodation on both islands esp since after mid April you may see rates coming down. There are B&Bs and apartments for rent.
Maybe look at the travel options since flying from TAB might be limited and you might have to go back to POS, this could influence your choice. Venezuela and Margarita Island are out of the question, pity since they would have been the closest and most interesting.

This is a tough one you'll find cultural experiences though different on both islands. It definitely depends on what additional activities you may be interested in. Barbados offers quite a bit to do, but not sure how nice it would be trying to experience everything in a few days, but at least you'll have plenty to choose from, including good duty-free shopping, great catamaran sailing tours and for cultural experience feel free to just get out and around go down to Bridgetown, a regular local restaurant etc. It really depends on what you prefer, more developed ( Barbados) or quieter options....

All the best in deciding

Barbados is a primer tourist destination.It is well developed and carters primarily to tourist from around the world.

As a solo/single traveler looking for great accommodations while on the island of Barbados that is close to most major attractions, including capital city Bridgetown beaches and more.

Check out

http://www.carmenscondominums.com/Solo-travelers-rooms-for-rent.html

I was originally considering Venezuela as well but it seems that flights to there are more expensive. Thanks for the feedback!

Grenada is divine! I love it and feel it's much less touristy than Barbados. Definitely would build in a boat trip to the Tobago Cays/Mayreau (and you'll feel like you're in that tropical desktop background that comes on so many computers). Would choose Grenada vs. Barbados for a solo, cultural experience, personally.

I can't comment on Grenada but I think Barbados would be perfect. I am a 26 year old female and just got back from there. I didn't travel solo, but I think you would be fine.

There is plenty of budget accommodation and Barbados has a great public transportation system. They have two types of buses, and vans. They both charge the same ($1 USD) and they will take you all over the island. I traveled in a group, but Barbados felt pretty safe. I didn't feel any less safe than I do at home. As long as you use common sense (and since you are a solo female traveler- avoid dimly lit, sketchy areas at night) you should be ok.

I would stick to the south coast of the island. It is more populated, the accommodation is cheaper, and the public transportation is more accesible (or so I hear).

I'm now leaning Grenada but public transportation is an important consideration for me as we'll. Is there a viable transportation in Grenada? I'd rather take public transit or a taxi than rent a car. I live in Brooklyn so I'm used to taking public transportation everywhere.

I always rent a car, it's much easier than getting taxis or trying to get public transportation, which I don't think there is much of.