DISEASE CHARACTERISTICS: - Diagnosis of neuroblastoma - Histological confirmation and/or demonstration of tumor cells in the bone marrow with increased urinary catecholamines - High-risk stage 3 OR metastatic disease - No stage 4S disease - Meets ≥ 1 of the following criteria - Recurrent or progressive disease at any time. Biopsy not required, even if partial response to intervening therapy - Refractory disease (i.e., less than a partial response to front-line therapy, including ≥ 4 courses of chemotherapy). Biopsy not required - Persistent disease after at least a partial response to front-line therapy (i.e., patient has had at least a partial response to front-line therapy but still has residual disease by MIBG scan, CT scan/MRI, or bone marrow). Biopsy (including bone marrow biopsy) of ≥ 1 residual site demonstrating viable neuroblastoma is required. - Evidence of MIBG uptake into tumor site within the past 4 weeks and subsequent to any intervening therapy - Adequate peripheral blood stem cells (PBSCs) available for autologous hematopoietic stem cell transplantation - At least 2 x 10^6 viable CD34+ cells/kg must be available (purged or unpurged) - Immunomagnetically purged PBSCs allowed - No CD34+ selected cells - No autologous stored umbilical cord blood stem cells - No allogeneic stem cells (other than PBSCs from an identical twin) PATIENT CHARACTERISTICS: - Lansky or Karnofsky performance status (PS) 50-100% required for study entry. - Life expectancy ≥ 6 weeks - Hemoglobin ≥ 8 g/dL* (transfusion allowed) - ANC ≥ 750/μL* - Platelet count ≥ 50,000/μL* (no platelet transfusions within the past week) - Serum creatinine ≤ 1.5 times normal for age as follows: - ≤ 0.8 mg/dL (for patients ≤ 5 years of age) - ≤ 1.0 mg/dL (for patients 6 to 10 years of age) - ≤ 1.2 mg/dL (for patients 11 to 15 years of age) - ≤ 1.5 mg/dL (for patients > 15 years of age) - Total bilirubin ≤ 1.5 times normal for age - ALT and AST < 3 times upper limit of normal (ULN) (for ALT, the ULN is defined as 45 U/L) - Ejection fraction ≥ 55% by ECHO or radionuclide MUGA OR fractional shortening ≥ 27% by ECHO - Corrected QT (QT_c) interval ≤ 450 msec - Lung function normal (i.e., no dyspnea at rest, pleural effusion, or oxygen requirement) - Not pregnant or nursing - Negative pregnancy test - Fertile patients must use effective contraception - Able to comply with the safety monitoring requirements of the study, in the opinion of the investigator - Patient and family must be physically and psychologically able to cooperate with the radiation safety isolation guidelines - Patient must not have a weight that would require exceeding a maximum total allowable dose of iobenguane I 131 at the assigned dose level (per institutional guidelines) - The study committee may discuss treating such patients at a lower dose level - Other ongoing serious medical issues are allowed provided they have been approved by the study chair before registration - No disease of any major organ system that would compromise the patient's ability to withstand study therapy - No history of idiopathic deep venous thrombosis, pulmonary embolus, thrombotic stroke, or arterial thrombosis - Patients with a history of central venous catheter-associated thrombosis that has completely resolved are eligible - No active or uncontrolled infection - Patients on prolonged antifungal therapy are eligible provided they are culture and biopsy negative in suspected radiographic lesions and meet other organ function criteria - No known HIV infection (testing not required before study entry) - No active hepatitis B or C infection NOTE: *Regardless of bone marrow involvement with tumor PRIOR CONCURRENT THERAPY: - See Disease Characteristics - Fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy - No prior iobenguane I 131 therapy - No prior vorinostat or other histone deacetylase inhibitors - No prior allogeneic stem cell transplantation - No prior total-body irradiation - No prior radiotherapy to the sole site of measurable or evaluable disease unless that site has demonstrated clear progression after radiotherapy - More than 12 weeks since prior myeloablative therapy with autologous stem cell transplantation - Patients who received stem cell reinfusion following non-myeloablative therapy are eligible - More than 30 days since prior and no other concurrent investigational medications - More than 30 days since prior and no concurrent valproic acid - At least 2 weeks since prior radiotherapy (12 weeks for large-field radiotherapy [i.e., craniospinal, whole abdominal, total lung, > 50% marrow space]) - At least 2 weeks since prior myelosuppressive therapy or biologic therapy - At least 7 days since prior cytokines or hematopoietic growth factors - No concurrent hemodialysis - No other concurrent anticancer agents, radiotherapy, chemotherapy, or immunomodulating agents - No other concurrent medications known to prolong the QT interval - No concurrent pentamidine prophylaxis for pneumocystis pneumonia - No medications that interfere with MIBG uptake for 1 week before, during, and for 1 week after iobenguane I 131 therapy