Top NITs like Surathkal, Trichy, and Warangal are considered close to if not at par with old IITs and definitely better than some new IITs.
Unless you are from the top IITs, admission to foreign universities for an MS does not depend on the college you are from. Many students from top IITs go to foreign universities every year. For non-IITians what matters is the project, internships, UG research quality, and extracurriculars. In fact, the sole reason IITians make it to top foreign universities is their strong determination and grasp of these aspects. Yes, the IIT alumni network does help you in the research internship but ultimately it’s your efforts that matter.
So even if you are not an IITian, keep working hard and you are likely to get admission to top foreign universities.
No, NITs are definitely not considered of the same level as the new IITs while applying to the US for an MS. But, the fact that IITs are the best brand in India and the second-best brand are NITs, is well known to the admission committees of most of the institutions.
Therefore, making it to top-notch universities is certainly possible; all that you need is good grades, a good GRE score, good SOP, and a few publications.