There are 2 daily direct trains from Szeged just across the Hungarian border. This train takes 2 hours, but only goes 45km, and costs under 200 Dinar. It is a single carriage local train and quite an experience.
There are direct trains running to Novi Sad.
Subotica's beautiful town house is surrounded with a number of pedestrian-only streets where people gather and meet, especially in the evening, giving the town a Mediterranean feel. The water-fountains and cafes in the center of the town are a great spot for people watching. The townhouse itself is lit up at night with spotlights that highlight the beauty of the building.
The town comes alive at night. The street Matija Korvina (off the main pedestrian street "Korzo") seems like the most happening, with a number of popular bars and restaurants (Boss, Stara, Beer&Co). In the summer there are many festivals of music, film, food, and any other excuse creative people can find. There is a large market about 2km west of the center called "Buvljak" or "Ocskapiac" (meaning flea market), where a morning can be gone in a flash. 8km to the east is Palic, an idyllic lakeside town of 6,000 people (take bus no. 6 to get there). The parks surrounding the lake are popular with tourists from the region.
The local dishes are definitely worth seeking out, as they are done really well and are quite cheap as well.
The region's famous fast-food is Burek. It is a pastry with various fillings like cheese, mince, mushroom, etc. It costs about 100 dinars (1 euro), a bit more with "tekuci jogurt" (a liquid form of savoury yoghurt). Most bakeries will have it, as well as specialized shops where it is made in front of you. An experience not to be missed!
Also worth seeking out is "chevapi", small skinless sausages served in a flat bread called "lepinje".
Grilled or barbecued meats are also a tradition, so they are done masterfully. Look for places displaying the sign "Rostilj"
If looking for full service, an upmarket ambiance and international menu, check out Boss Cafe in the center of town; is a really nice place to spend time and the pizza is excellent. (http://www.bosscaffe.com/)
Since the region grows a lot of fruit, a lot of households make snaps ("Rakija") from the various stone fruit, apples, pears, grapes, etc. grown locally. Try to find some that was made for own consumption (and not for sale) for the best quality! Another local specialty is a bitter herbal liqueur called "Gorki List" (various knock-offs are called Pelinkovac, as they are all made from the herb called Pelin, but this is the real deal). It aids digestion, so drink it some time before the meal.
There is a hostel with clean modern private rooms for 900 Dinar per night. It is behind the station, Segedenski, behind the Economics Faculty at number 14. The tourist information can supply maps and directions too.
Take Bus No.1 (in front of the train station) to Kelebija granica (the Hungarian border). From the border you can walk to Tompa Bus station and take busses from there to Szeged, Pécs (via Baja) and Kiskunhalas.