Since you live in the city and are out and about at playgrounds, I'd also get the $ 10 portable potty (excuse me, «potette») from the website or Buy Buy Baby so you and your babysitter can have it along at the playground. (askmoxie.org)
I carried a potette around with me for years once mine were potty training. (chelseamamma.co.uk)
, the Ikea potty (cheapest option), or the potette potty (my favorite) is easy to keep in your car or even your diaper bag. (organicbabyatlanta.com)