Well, certainly avoid the amphitheatre (which I swear is more vertiginous than it used to be). What about stalls circle? It really depends on how bad the vertigo is, and whether it only occurs when you're looking over a big drop. The balcony only has 3 rows (I think), so if you were sitting at the back possibly things might be better?
I agree, the Stalls Circle is quite a good idea. My mum and I used to go regularly, and would tend to sit in the Sides Row A for opera, and more centrally in the Stalls Circle for ballet. You are only very slightly higher than the back rows of the Stalls, so hopefully there should be no vertigo problems.