Hi Joelle935 - sorry to hear you're not feeling very confident and a bit lonely. I totally know how you feel. It is tough moving to a new area with a little one. You've moved to a great place - there is such a nice, friendly community of mums and dads here. Here are a few ideas for places and groups you could try:
Exeter Forest School - I met some lovely people at this group. Great for age 3/4 too: www.exeteroutdoors.co.uk/exeterforestschool/toddler-club/
You can find lots of toddler and baby groups here: local.mumsnet.com/exeter/baby-toddler-groups
The Exeter Phoenix is a hub for mums - they have family Saturdays with lots of activities (take a look at their website). They also hold Pyjama Drama sessions on Thursday and Friday mornings. These are paid classes - but another nice way to meet local parents and entertain your LG. I don't find the sessions intimidating at all (although Exeter Phoenix itself is a bit cool!)
I love going to RAMM during the week - it's a friendly museum with a nice cafe. Your LG can pull around one of their fun suitcases which has fancy dress and activities in it.
There are various NCT coffee mornings - might be worth sending them a message on Facebook for an up to date list.
Are you on Facebook? I'd recommend joining the Mums in Exeter group - nice, friendly group and you can post questions there too.
I know that Mumsnet Exeter are going to be planning meet-ups for parents - so keep an eye out for these. You can sign up here: local.mumsnet.com/exeter/group-meet-ups/exeter-centre
Hope this helps. I'll have a think about more places and get back to you. I'm not sure whether you're new to Devon, or just new to Exeter? I have to say Devon is one of the friendliest places I've ever lived - don't be shy to start up conversations with random mums because I reckon you'll get a friendly response. I often go to places around Exeter on my own with 2 boys, like: Dart's Farm, Bicton Park and Orange Elephant Ice Cream Parlour (all great places for your LG) - and usually manage to have a friendly chat with another mum or 2.
xxx