The easiest places to travel when you only speak English are English-speaking countries. While this option obviously won't teach you much about foreign languages, it will require less mental labor on your part if what you're looking for is a relaxing vacation and not an education in language. English is the official language in Australia, New Zealand, all the countries of the UK and most of the islands in the Caribbean. In addition, English is widely spoken in South Africa, India, Belize and the urban areas of most European countries
Whatever country you decide to travel to, there is likely to be a wide variation in the amount of English spoken in different parts of the country. Cities and locations that attract many tourists will always have more English speakers around. This doesn't necessarily mean that you will be safer in these areas than in other areas where no English is spoken, but it will be easier to make yourself understood. Remember that when it comes to crimes such as pickpocketing, the presence of many wealthy foreigners and English speakers may actually increase your chances of running into trouble.
When people think about travel safety, they often fear being robbed or attacked. In fact, the most likely misfortune to befall you in a foreign country is illness. Because your body isn't used to the particular foods, micro-organisms and water types that are present in foreign places, you are more susceptible to giardia, salmonella and a host of other food and water-borne diseases. Your linguistic skills won't protect you from these, except in the sense that you are more able to determine exactly what you are eating and drinking if you speak the local language. If you only speak English, either avoid uncertain food sources or hire a fully bilingual local guide to help you out.
If safety from crime, illness, injury and getting lost are your primary concerns, you are probably best off going to a resort. Resorts that cater to English speakers and wealthy foreigners exist around the world, providing supervised areas, safe food sources and familiar environments. You probably won't learn much about the local culture or have any unexpected adventures if you don't leave the resort, but it is a place where speaking only English won't get you into trouble.
