You would probably have to go with an older tube type rig. All solid state rigs most likely will be rendered to "toast" in a nuclear explosion or nearby EMP. Its interesting, I have had several non-hams ask me this question in recent years.
All solid state rigs would not most likely be rendered toast as a result of “nearby” (need to quantify that) EMP or nuclear explosion. EMP is often over rated as a hazard. To be sure, it is a very real issue, but not quite the all-powerful electronics-ending event that many people take it for.
For sure, solid state and even tube type radios connected to antennas or the power mains will be very likely to take substantial damage in the event of either event. Radios, either hollow state or solid state, not connected to antennas or power sources are going to be much more survivable. Radios stored in even a moderately hardened or shielded container will be most likely to be unaffected by the described events…assuming they are far enough away not to take shock or thermal damage. But, if they are that close you have other issues.
Many preppers have taken to storing radios, when not in use, in metal containers. In all probability this will protect against all but the largest possible very close EMP. And even then I would bet many will still work. Even a heavy foil wrapping around a handheld in a bug out bag should increase survivability.
The results of the American Starfish Prime and the Soviet Unions K Project are generally pointed at as the best examples in open literature to draw from as models.
In Starfish Prime a dense population zone 900 miles away from the High Altitude EMP (HEMP) experienced relatively light damage from the EMP, a small percentage of streetlights were damaged and some telephone gear, for example. There were no reports of damaged radios, even ones connected to antennas at the time. This was in 1962, and although solid state radios were in the minority they were in use by then.
The K Project was an intentional HEMP conducted directly over a populated region. It caused much more extensive damage to infrastructure (for example a major power station caught fire and burned to the ground as a result of the event) and there were several reported radio casualties. However, such reports of radio failure were relatively few. To be sure, in that region of the world, tube type radios were almost all that was found at that time period.
The OP does need to give more details if he wants meaningful answers. What are your goals for such a radio? What distances and with who do you expect to communicate? Portable? Handheld? Mobile? Etc.
T!