There is a large pedestrian zone in Novi Sad. The pedestrian zone consists of Zmaj Jovina, Pašićeva, Svetozara Miletića, Laze Telečkog, part of Danube streets, Katolička porta and Freedom Square. In this area of the city you can see most of the Novi Sad monuments, beautiful and old building, cafés and pastry shops and clubs.
Its very easy and most important of all, interesting to explore Novi Sad all by you're self and there are many apps to guide you, for example I love Novi Sad and Novi Sad Stories which you can download for free in Google Play store.
If you like to explore the city with a professional guide, don't worry, there are many organized FREE walking tours.
The cheapest way of transport in Novi Sad is by city buses. The buses routes and timetables are set at every bus station, but for everyone who like to check it in advanced they can find it here.
Ticket for one ride in city buses are 55 RSD (location is irrelevant as long as you don't change the bus), and you can buy them from the bus driver.
You can get a daily bus ticket which cost 278 RSD.
By the Western Standards, taxis are not very expensive, the minimum fare varies between 80 and 100 RSD. And for a cross-city fares the cost is about 150 to 200 RSD. The language barrier is not a big problem, because many taxi drivers in Novi Sad speak English very well.
Allways travel with taxis from good companies such as: Pan, Vojvodjani, SOS, Delta, Novus, Naš and Lav. You should be careful with taxis companies that are not on this list, because you may pay up to four times more than your fare should be.
The cycling route EuroVelo 6 connects Novi Sad to Hungary and to Belgrade by following the Danube river. Novi Sad has dedicated cycle-paths along most of its avenues.