I would suggest two areas - or you can combine both of them, depending on the duration of your stay, and whether you prefer to move around, or to stay longer in one place.
One suggestion is to visit Istra - the peninsula in the northern part of Croatia. It has some beautiful cities dating back to ancient Roman times: Pula, with large Roman Arena, Poreč, and Rovinj, and Brijuni (Brioni) islands - you can take a day trip to Brijuni by boat from Pula. All of these cities are on Istrian coast. I personally prefer the mainland Istra, with very beautiful forests and medevial cities such as Motovun, Buzet, Roč, and (allegedly) the smallest city in the world - Hum.
The other suggestion is to travel by bus to Zagreb and spend a day in Zagreb (the capital). Then take the bus to Plitvice lakes and spend a day in Plitvice enjoying the beautiful nature for a day, and in the afternoon take the bus from Plitvice to Zadar. (check bus schedules ahead and plan your trip!). Zadar is very beautiful and you can visit beautiful Kornati islands (boats take you for a day trip to Kornati from Zadar), or you can visit islands of Pag, or maybe spend a day in Šibenik, which are all near Zadar, and well connected by bus lines. Or if you want to enjoy more hiking, visit Paklenica park near Zadar.
There are some other very beautiful places in Croatia: Islands of Hvar, Vis and Korčula - but these are further away and it will be more expensive and take longer to get there. Dubrovnik is, if you ask me, overrated, too expensive and crowded with tourists. If you want to see medevial/ancient stone walls, check arena in Pula or fortresses in/around Šibenik, or Zadar center/peninsula.
To save the money, plan everything ahead, try to find affordable accommodation, check bus schedules before. Food in Croatia is somewhat expensive in fancy restaurants, but pizza places (Pizzeria) are relatively cheap, you can get a big pizza for around 5–6 Euro. There are also many bakeries in Croatia (Pekara/Pekarnica) where you can buy burek with cheese or with meat for around 1.5 Euro, and some better Pekarnica also have sandwiches for around 2 Euro (but burek with meat will feed you better than sandwich).
Have a nice stay in Croatia!
