Here's some recommendation for direct admission in Ph.D. Sanskrit without appearing in NET:
- Central University Of Haryana (CUH), Mahendragarh, Haryana: In this institute you need to appear in their college entrance exam including a small interview. NET is not required for Ph.D. Sanskrit, also this institute is best option near NCR.

- Sanskrit University, Mathura (UP): They also offer Ph.D. Sanskrit through their own university level entrance exam including Interview. Required that percentile of MA should be more than 55%.

- JRRSU, Jaipur: This one is the best local option in Rajasthan, offers you a Ph.D. Sanskrit with some merit basis. There are some eligibility criteria you need to check on their official page or contact them directly for any query.

Recommendation is that NET/JRF are the best entrance exam to clear and to get admission in reputed institute, because mostly institute have considered one of these exam mandatory.
Even though You can apply for Ph.D. course with 4 year UG + 75% with master's directly in some institutes, some have still didn't mandate master's degree.