DNA is charged negative. Where is all the positive charge in my body?
DNA in the body is not available as a free molecule, it is organized around DNA binding proteins, mostly the histone octamers. These proteins carry positive charges (mostly from lysine side chains) which interact with the phosphate backbone of the DNA. It is like in the figure below, the charges play an important role in the tight packaging. See here for more details.



The charge (or the temporary neutralization at some points of the DNA) is also important for the regulation of the DNA. Acetylation neutralizes the histone tail and loosens the DNA-protein structure (see here for more information).

Positively charged ions don't play a role in neutralizing the DNA charge in living cells (this is different for precipitations), as both are solubilized and split into ions. The concentration of positively charged ions like sodium and potassium are tightly controlled by the cells, as they are important for the function of transporters (for example the sodium-glucose transporters and others) or for keeping up membrane potentials. Moving the ions, which have to neutralize the DNA charge around would lead to a polarized nucleus.