Obviously this is the Durham forum, so don't expect unbiased views.
I'm a graduate of Durham (Trevelyan College) and am still involved as a member of the Senior Common Room and as a College Mentor (although please note I'm speaking personally and not as a representative of any organisation or employer!)
I also took a look at Bristol and went for an interview back in 2001 when I applied for Universities, but I didn't put it as one of my choices, either firm or insurance.
Durham (and Trevelyan in particular) offers a small friendly community, which has both advantages and disadvantages. If you were looking for a major party city with clubs through till morning, Durham isn't going to be the place for you (although Newcastle is only a 15min train away), but if you'd rather be in a place where there is a whole support structure built from the ground up to help you settle in and thrive, I don't think that anywhere does it better.
Personally, I love the place. It's big enough that you can find the shops and facilities you'll need day to day but small enough that you aren't lost in the crowd. The transport links are also good, with trains to London, Edinburgh, and cross-country to Bristol.
When it comes to your decision, only you know what's important to you, but I'm sure people will be happy to answer any specific questions you may have.
Finally, whilst it may seem that you have no backup plans, or 2nd chances; small set backs at this stage in your life are just that, not insurmountable disasters. I got into Durham twice, once just after 6th form, and once after I'd messed up my degree, dropped out and re-applied. If you don't get the results you're looking for this summer, there is time to apply again with your results in the bag for the 2016/2017 entry.