Inclusion Criteria:
* Age \>= 18 years old
* Histologically-confirmed primary uveal melanoma
* Definitive local treatment for primary tumor, including surgical resection (enucleation) or radiation therapy (radioactive plaque or external proton beam)
* High risk for distal recurrence defined as any of the following conditions: A) Confirmed both monosomy 3 and 8q amplification; B) Class II tumor
* Less than 6 months from the date that local treatment (surgical or radiation) of the primary tumor was finalized
* Karnofsky performance status (PS) scores of 70 or greater
* If female, no pregnancy
* If of child-bearing potential (\< one year post-menopausal), must agree to practice an effective method of avoiding pregnancy (including oral or implanted contraceptives, intrauterine device, condom, diaphragm with spermicidal, cervical cap, abstinence or sterile sex partner) from the time informed consent is signed (women only) or the time of initiation of sunitinib (sunitinib malate) (men only); both men and women must agree to continue using such precautions while receiving sunitinib or valproic acid and for 30 days after the final dose
* Absolute neutrophil count (ANC) \>= 1500/mm\^3
* Platelets \>= 100,000/mm\^3
* Hemoglobin \>= 8 g/dl
* Serum creatinine \< 1.5 times upper limit of normal range (ULN) or creatinine clearance \>= 40 ml/min
* Serum bilirubin \< 1.5 times ULN
* Serum albumin \> 2.0 g/dl
* Adequate cardiac function (ejection fraction \[EF\] \> 50%) based on multi gated acquisition (MUGA) scan or 2 dimensional-echocardiogram (2D-Echo)
* Life expectancy of at least 5 years
Exclusion Criteria:
* Other malignancy within 5 years, except curatively treated non-melanomatous skin cancer, curatively treated carcinoma in situ of the uterine cervix, or early stage (stage I or IIa) prostate cancer
* Metastatic uveal melanoma
* History of severe allergic reaction to sunitinib or valproic acid; inability to receive sunitinib or valproic acid
* Previous treatment with sunitinib or valproic acid for uveal melanoma
* Active treatment with valproic acid for non-oncological conditions, if this cannot be safely switched to an alternative agent
* Active epilepsy or convulsive conditions that require continuous use of anticonvulsants
* Patients with known urea cycle disorders (i.e.: ornithine transcarbamylase deficiency)
* Severe cardiovascular disease within 6 months, including myocardial infarction, severe/unstable angina, coronary/peripheral artery bypass graft, symptomatic congestive heart failure, cerebro-vascular accident or transient ischemic attack, pulmonary embolism, life threatening arrhythmias, uncontrollable hypertension or QT prolongation syndrome
* Active liver disease (i.e., cirrhosis, viral or autoimmune hepatitis, etc.)
* Pregnancy or unwillingness to stop breast-feeding
* Prior myelosuppressive chemotherapy or other investigational drug therapy within the last 6 months prior to initiation of sunitinib or valproic acid
* Current evidence of hematemesis, melena or gross hematuria
* History or presence of any significant bleeding disorders
* Concurrent use of a strong cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) inhibitor or inducer; these medications should be discontinued or switched to a different medication with a weaker CYP3A4 interaction prior to enrollment into the study; if patients need to continue the same medication(s), they are excluded from the study
* Chronic usage of aspirin greater than 81 mg/day
* Unable to render informed consent and to follow protocol requirements
* Any other medical condition(s) that, at the discretion of the principal investigator (PI), would make the patient inappropriate for this study
