**Core Concept**
The patient's presentation of painless gross hematuria and a filling defect on intravenous urography (IVU) suggests a urothelial malignancy, specifically a renal cell carcinoma (RCC) or a ureteric tumor. The location of the filling defect at the lower pole of the infundibulum is more suggestive of a RCC.

**Why the Correct Answer is Right**
The next best investigation to be done in this case is a contrast-enhanced computed tomography (CT) scan of the abdomen and pelvis. This is because CT scan provides detailed information about the size, location, and vascular supply of the tumor, which is essential for planning the management. CT scan can also help to differentiate between a RCC and other types of renal tumors or tumors in other parts of the urinary tract.

**Why Each Wrong Option is Incorrect**
**Option A:** Ultrasound is a useful tool for assessing renal morphology and detecting hydronephrosis, but it is not the best investigation for characterizing a filling defect on IVU. Ultrasound is also operator-dependent and may not provide the same level of detail as CT scan.
**Option B:** Magnetic resonance imaging (MRI) can provide detailed information about the tumor and surrounding tissues, but it is not typically the first-line imaging modality for renal cell carcinoma. MRI is also more expensive and less widely available than CT scan.
**Option C:** Renal angiogram is not the next best investigation in this case, as it is typically reserved for patients with suspected renal vascular disease or for preoperative planning in cases where embolization is planned. In this case, the primary goal is to characterize the tumor and plan management, not to evaluate the renal vasculature.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that painless gross hematuria is a classic presentation of urothelial malignancy, and any patient presenting with this symptom should undergo prompt evaluation with imaging studies to rule out a tumor.

**Correct Answer:** C.