Hi, Federica. In my experience (and in the literature), carbon nanomaterials only form a suspension if strongly agitated or sonicated, even if you add some surfactant on it . If you can't use surfactants, the suspension may be done immediately before the  exposure, because the particle aggregation dynamics is normally quick. Moreover, the salts in the culture medium of the cells accelerates the aggregation of the nanoparticles. You must characterize the suspension, and you may know that just part of the particles are nano-sized, which rapidly aggregate with time.

Ionic liquids are known to disperse graphene (at low concentrations).. and some choline based ILs are known to be bio-compatible. 

Ionic liquids，ClSO3H

I suggest you use certain types of biocompatible dispersants, such as serum albumin, some ionic or non-ionic copolymers, including Pluronic F108. All these dispersants are biocompatible below certain concentrations. They are effecient in dispersing carbonaceous nanomaterials including graphene. The mechanisms envolved are that these dispersants can provide either electrostatic or steric hindrance or both to maintain the dispersal status of the particle suspension.

You can find more detailed info in some of my papers. Let me know if you need more. Thank you.

Any aromatic solvent could be able to exfoliate GNP into single- or few-layer graphene under sonication... however, if you have to use them for biological applications, take into account that toluene and other common organic solvents are not suitable. Use biocompatible surfactants or essential oils plus ultrasonication (at least 3-4 hours). ps: you will achieve dispersions, not solutions.

People looking to disperse graphene in solvent typically using dimethyl formamide (DMF) or n-methyl pyrrolidone (NMP). The cyclic ether tetrahydrofuran (THF) is also an option, but is less advisable based on its volatility and reactivity with plastic in my experience. You would first typically need to bath-sonicate or probe-sonicated the dispersion. If you do not want to end up with aggregates, you should leave the dispersion to settle or even centrifuge it lightly to let the aggregates crash out of suspension. This is more or less how people typically do it in my experience. 

However, there is a host of other ways in which people claim to have been able to disperse graphene in literature, and I include a couple of them below for your reference (I especially selected ones which focus on water or water-like organic solvents for your bio-application):

 http://pubs.acs.org/doi/abs/10.1021/jp1037443

http://www.spm.com.cn/papers/0242.pdf

http://pubs.rsc.org/en/Content/ArticleLanding/2010/CC/c0cc02688c#!divAbstract