There are plenty of touristy sites around Baku. Sadly, they're not well served by public transport, and with our limited time inbetween going to the Eurovision shows, we only saw the sights of Baku and went up to a former major Soviet industrial town, Sumgayit, some 30 kilometers north of Baku.
The old town of Baku is centered around the impenetrable Maiden Tower, and this is one of the few remaining oldskool attractions in Baku. Baku is primarily impressive for it being something of a mix of Tehran, Dubai and Kuala Lumpur, with the city's gorgeous boulevard, hypermodern architecture and beautifully refurbished facades.
The flame towers, lording over town from one of its hills light up in gorgeous polychromatic displays.
Haider Aliyev's grave is relatively understated.
Benno and I went of a fact finding mission to Sumgayit to see whether Azerbaijan's superficial changes were specifically done to impress visitors coming in for Eurovision. No one really visits Sumgayit as a tourist, but here, too, we found a lot of recent and in progress refurbishings. We even walked along the shore, Sumgayit is on the Caspian, to discover the towns decaying industries, but only found recently refurbished factories.
Apparently, decaying Soviet monstrosities still exist, but it seems they are slowly being replaced.