motivation (or lack of)

I ran my first half marathon a couple of weeks ago and since then I've felt demotivated. After a few days off I've managed three runs and a couple of light cross training sessions at the gym. After my last run of just over 3.5 miles it was a struggle to be bothered with the cool down and stretching. 

Maybe I need a new goal or something?

You don't need to find the motivation to do something. You just need to do it!

However, what you describe is common. Yes a new goal may be good, but it doesn't have to be time or distance based (but it could be). Could be about running in new places/off-road etc. Could be the goal of running a certain number of times a week. could be just to enjoy running for the sake of running. Could try the naked runners approach (not clothes, just no gadgets - check out their website).#

How about joining a club?

I never cool down or stretch after a run.

I'm exactly the same 10kay. I think it's hard to shift from being focussed on acheiving something to not being quite sure what to do. Also doesn't help that several people have asked when I'm going to try a 'full' (answer: not any time soon). Plus I think the dark evenings have also deterred me. 

Have you tried doing different types of sessions? I did my first ever interval session last night (of sorts)- I was a bit bored of my run so just started to mix it up a bit by doing sections at different paces and it really helped me. I've also decided that my goal for now is to improve my 5k (parkrun) time over winter and hopefully get a new 10k PB in February. I'm also looking forward to doing some really unstructured runs i.e. just go out for a run to somewhere without thinking about how the mileage fits in with a training plan. 

I've been for 1 run in 12 days since my marathon.  Hoping the daylight tomorrow entices me out.