Pontianak is a good stopping route for two reasons:
1. Its has a land transport that goes to Kuching, capital of Sarawak (Malaysia). The travel time is approx. 6-8 hours daily, and in quite a number of bus company running the route. The cost is around Rp. 130,000 per person.
2. Its has a direct air transport to Singapore, via Batavia Air at around Rp. 900,000. The travel time is approx. 1 hours and air tickets around Rp. 900,000. As well air transport to Kuching in half the travelling time and cost to Singapore.
If you like to land yourself to the third largest island on Earth, Western Kalimantan should be a better choice rather than go to the Eastern for those both reason above. It can direct you to Sarawak, which is a better organized site for tourism.
Now, after you landed on Pontianak airport, Supadio, the only transport reliable to back to the CBD of Pontianak is via airport taxi, which is around Rp. 50,000/trip. In the CBD the standard hotel will be cost very cheap due to IDR against your western currency. Pontianak don't have the vibe of backpacking hostel style accomodation yet, (it has, but mainly a homestay or for business salesman from other island of Indonesia, mean it can not accomodate even an English speaking services).
The public transportation is quite an amaze, for it's almost will not serves foreigner/outsider well. This is due to the lack of information on the public transportation without asking around. The city commuting transport is a small colorful mini van, which is named as "Penjara", "Gajahmada", "Jawi" route rather than numbered. And most of it differentiated by its color. So if you plan to travel via this mini van, try to research by asking around. The cost is very cheap.
The other alternatives is travelling a short distances via the tricycle, or "becak". The concept is similar to a taxi, which you can ask to transport you to your destined addresses. And finally a city cab is available as well.
Now, what should you do in Pontianak. While the beauty of Western Kalimantan mostly can be enjoyed outside Pontianak (the western coastal site is the recomendation), the city itself is a small busy in economic activities. So less tourism site around, .... but , if you enjoy street walk, and cuisine (mostly Chinese cuisine is well representated here), try to walk around the Jalan Gajahmada , Jalan Tanjung Pura dan Jalan Pattimura for city viewing. These roads will have lots of street food that cook original and authentic local foods.
And if you really get lost in the city (or doesn't even understand what I'm writing), just type in a comments, and I will answer for you. Or even organized a city viewing..... for foreigner only.
Kapuas River, one of sceneries to look up in Pontianak