If the weather is warm and sunny and you’ve taken the ferry to reach the Asian part, just take a minibus or taxi to go to Bostancı Seaside (Bostancı Sahili) for a long walk and a picnic.
At Bostancı seaside, everything is colorful, and many dogs are playing and running around. You can take your drink (maybe wine or beer?) with a sandwich or some cheese from the supermarket (Migros) and cross the street to find a shadowy part in the meadow. Play a song from your phone, drink or eat while you are looking around. You can even have a short nap.
In the same region there is a long street called Bagdat Street (Bağdat Caddesi) and you can shop, eat or drink something there too. Especially Turkish and global brands have the biggest places there.
If you are looking some little gifts, there are lots of local shops too. Prices may be a little high because Bagdat Street is the most popular region as well as a touristic spot.