There are training jobs in psychiatry available all over the UK. You will apply for training posts in a particular region and then have placements in different locations within that region. You can apply for your foundation, core and higher training all in the same region meaning that, assuming you are successful, you can settle in one particular area of the country.
Part-time/less than full-time training
The BMA provide information on different working patterns including training less than full time.
You can undertake research alongside your clinical commitments at any point during your career. You can also choose to undertake formal academic psychiatry posts, for all or part of your training. These posts (academic foundation programmes, academic clinical fellowships and clinical lectureships) combine research with clinical training.
As a trainee you can apply to take time out of your training programme allowing you to travel. This could be to undertake work that would count towards the completion of your training or as a career break.