Spectrum analyzer?

Depends on your needs. In general, RTA is not the best tool for speaker/room interactions. The starting place for RTA is TrueRTA.

However, the best combination of capability and price is RoomEQ Wizard which is a freeware program. You will need a mic, a preamp/soundcard and a PC, though.

There are other options if you have specific requirements.

Kal

The spectrum analyser in the Behringer DEQ2496 will do the job for about $350 (including the microphone). 1/3 octave.
What's more, it can fix your problems once you have figured out what they are.

1/10 octave or better can be achieved by both TrueRTA and by REW.

The reason that RTA is not useful is that it has little memory while the major room influence is in the delayed reflections and their interactions. For that, you need to see "waterfall" plots or similar that show how the sounds at different frequencies decay in the room. Generally, one wants uniform decay of all frequencies.

For more info, I recommend Toole's new book "Sound Reproduction - Loudspeakers and Rooms." I am about half way through it now.

Kal