I hope you are ready...
Prepare yourself for what you are going to see... You will be going to the poorest area of an already very poor country.
I hope it's not the first time for you to see people living in very inhumane conditions... If you haven't, I urge you to do your research so you don't get the shock of your life...
Now, assuming that you know what you're getting yourself into, get in contact with that guy that porfirio_rubirosa is suggesting, it would be wise to get into that adventure with people that might know the area and speak the language.
I don't know how much time you've got, but these are the areas I know and I recommend:
Start from the south... Visit Barahona, mi personal favorite area of the country... Visit Para?so, Enriquillo and Bah?a de las Aguilas (and see what all that fuss is about - breathtaking!).
Start the bother from Pedernales up to Jiman?, this is where the adventure begins and you'll notice the drastic change in scenery... From dry and deserted Pedernales to the greenery of the mountains of "Cordillera del Sur" and back down do the desert. Once you reach Jiman? Visit the Lago Enrriquillo, it's absolutely worth it!...
The road (the last time I checked, like 10 years ago) was terrible...
I don't know if they've fixed the road from Jiman? to Comendador, but back then we had to go back to Neiba and from there to San Juan de la Maguana and from there to Pedro Santana, to take "Carretera International" that goes along the border until the town of Restauraci?n. If you want to skip Barahona, you can start running the border from that point, but you'd be missing half the fun, though.
The views on this road are spectacular! But it will easily take you 4 hours to do 100 km! This is where you'll see the stark difference between the two countries.
Finish in Dajab?n and reach the north coast by Monte Cristi and if you can, go along the north coast to the east.
If you want to do this right, take at least a week, you can find very basic, but clean accommodations in the towns of Pedernales, Jiman?, Pedro Santana and Dajab?n.
You'll find numerous rivers to swim in and places to stop and eat, grab a bear or hear amazing stories from locals... If you don't know where you are going, do not venture into Haiti, stick to the Dominican side of the border.