Caffeine dissolution
Caffeine is not acidic. In fact, it is basic. It will raise the pH of water to some degree. It is a weak base, so the free base will exist in equilibrium with its protonated counterpart.

Due to its basicity, it will be more soluble in low pH aqueous solutions than in high pH solutions. This is because in low pH solutions, caffeine would exist completely as a protonated salt, making it more hydrophilic. Despite this, caffeine is very polar and is still quite soluble in water at higher pH levels.

The six-membered pyrimidinedione can exist in an aromatic, zwitterionic form where both amide nitrogens have formed double bonds to respective adjacent carbonyls. This six-membered ring had been observed as being planar. Therefore, it has been concluded that caffeine does indeed exist primarily as its zwitterionic resonance form, with two positive charges and two negative charges. The negative charges exist on the two carbonyl oxygens. These may be slightly basic, too, but significantly less so than a structurally similar hydroxyphenol (e.g. resorcinol) due the electronegative nature of the attached aromatic ring. Therefore, the basic imidazole nitrogen likely has largest effect on the pH.

The fact that there is possibly more that one weakly basic atom on the caffeine molecule complicates calculations as far as determining a theoretical pH. Also, the calculation would require the quantity of caffeine you will add. If you need an exact number, you will have to measure it. You can be sure, however, that the pH of the water will rise as caffeine is added.