On the UNESCO World Heritage List, Baku's compact old city core is a delightful layered maze of medieval alleyways set behind fortified stone walls on three sides. The lanes and passageways are lined by a plethora of historic buildings of very varying ages.
If you have just 15 minutes: stroll down Zeynalli Street, catching a glimpse of the mysterious Maiden Tower (add 20 minutes and a fee to climb it for great views), colourful carpet peddlers amid ancient caravanserais, medieval mosques, century old mansions and an archaeological site. If you have an hour: extend your stroll though some more lived in' parts of the old city, see the powerful Double Gate and follow the battlements around to the 15th-16th Century Shirvanshahs' Palace complex (add around forty minutes and an entry fee to look around - limited exhibits inside)
If you have two or three hours: Do one of the self-guided audio tours giving oodles of information on a range of the sights within the city. Or extend a basic stroll further into the maze and stops at various shops, cafes and art galleries both within the walls and just outside. If you have trouble walking: There are electric buggies starting from near the Maiden Tower that can buzz you around past all the main attractions within Icheri Sheher.
Easy to combine with: Oil Boom walk, Fountains Square, State Art Museum, Nizami Literature Museum, Baku Boulevard, Funicular.
There's no better way to get a feel for Baku's relaxed, Mediterranean atmosphere than by strolling along the sweep of promenade that follows Baku's Caspian waterfront on a gentle arc past the whole length of the central city area.
If you have just 15 minutes: Drive along the coastal road to get a quick glimpse of the grand buildings that line it. Or nip across that busy road via the underpass from beside the Four Seasons Hotel and admire the sweep of bay from behind. If you have an hour: Walk the section of promenade between Dom Soviet and the Carpet Museum.
If you have two or three hours: As above but with a café stop, visits to Park Mall and the carpet museum plus a pleasure cruise on the Caspian.