"Are credit cards (Visa) readily accepted in the DR to pay for trips and the odd meal out?"
YES
Would it be easier for me to bring an amount of cash in US dollars?
YES
Would it be easier for me to bring USD travellers cheques?
YES if you have a passport
Credit Card fraud is a growing business in the Caribbean, be careful.
Read this information sheet on money in the DR.
http://dr1.com/travel/expect/money.shtml