Usually go on holiday by myself, and thoroughly enjoy it. Went to Washington D.C. for a week and just adored being able to take my time going round the museums and attractions.
This year went to Zambia and Botswana. Met loads of nice people in Zambia (place I stayed at was full of honeymooning couples), but went out on my own to join in group activities such as white water rafting and walking with lions. In Botswana, went on a week's horse riding safari, again met loads of nice people from different countries, and rode some fantastic horses. Later this year, will be travelling on my own to New York to do the marathon.
In short, just go and enjoy yourself! If you don't feel entirely comfortable in restaurants, take a book with you to read between courses.