EMB100 pilot on IFR flight plan reports requesting the RNAV (GPS)-B approach to HND and is told by LAS Approach that the approach is unavailable due to the missed approach conflicting with LAS arrivals. IFR is canceled but the VFR approach is botched and results in a go around to a left downwind. Turning base a TAWS alert results in an aggressive climb and penetration of the Class B above. Reporter elects to divert to LAS.

Narrative

Flying into HND; an unfamiliar airport; at night after an afternoon departure on the east coast; we were on an IFR flight plan. We were on the NOOTN One arrival when we asked for the RNAV (GPS)-B approach. We were told by ATC that she could not give it to us because the missed would conflict with arrivals at LAS. She did not offer an alternate missed approach procedure. We asked if the Tower and airport were open and we were informed that the airport was open but that the Tower was closed. ATC then asked if we would like to cancel and complete our flight VFR which we did. It took several attempts before we were able to activate the pilot controlled lighting at HND. When we finally did; we discovered that we were too high and too close to the airport to make a stabilized approach to landing and decided to go around. We made a left turn; climbed in a spiral and headed upwind [downwind?] parallel to the approach track. On turning base we got a TAWS alert to pull up. We did so rapidly and climbed. This put us into Class B airspace. We contacted ATC to let them know about our terrain warning and request IFR clearance to LAS. When taxiing to the FBO; we were asked to call the TRACON. Contributing factors were night conditions; fatigue; unfamiliar; mountainous terrain; failing to insist on an instrument approach. Human factors included the Air Traffic Controller's failure to give an instrument approach to an instrument rated pilot in an instrument equipped airplane on an instrument flight plan.