Fiona West's reply:
Museums and cultural organisations frequently require individuals with administrative, research and social media skills. The best thing to do is to take a look at some of their websites. They often advertise vacancies and so you may find it useful to see if they have any of these roles being advertised at present, in order to identify what they are looking for. If they do have these roles on offer then take a look at the core skills they are requiring and consider how the experience in your role can be linked to these.
It can be useful if you reflect on your current CV and the skills / experience you have. So often, people can become pigeon holed by thinking they need to apply for the next role in their chosen field (e.g. from administrator to senior administrator, etc). Instead be prepared to think creatively when looking at the roles organisations offer to see if something may just need the experience and knowledge you have. Look at the skills they are requiring - it may be that the skills they need (for example, for a project or research assistant vacancies) may well apply to what you can offer.
Good luck with your job hunting.