Things to do in the DQ on Sunday? (Riyadh)

Hi
Just moved to Riyadh. I'm a Nanny for a Private Family so except for my day off I don't get the chance to explore much outside the family compound.
I'm keen to take some time out on my day off, which is Sunday (tomorrow) and perhaps visit a coffee shop and explore in peace a little bit.
Somewhere where I can perhaps be around some fellow native English speaking Ex Pats would be a huge bonus as I'm the only English speaker at work.
I've had lots of invites out through this site from some men which is very kind but I'm not feeling confident enough to meet up with anyone of the opposite sex just yet, I'd just like to drink a coffee in a safe and friendly place :)

Any suggestions welcome, I went to the Diplomatic Quarter earlier this week but just got hopelessly lost!