Sorry djp_syd, Gràcia is NOT in l'Eixample, they are two different neighbourhoods pertaining also to two different districts, yet they're indeed "neighbours" ;) DISTRICTS: http://bit.ly/BCNdistricts -there are 10 in the city and NEIGHBOURHOODS: http://bit.ly/BCNhoods -there are 76 in the city. I however concur with all your other comments. Adding also that the area south of Gràcia -the one bordering with Diagonal- is probably the more convenient, or else, somewhere near the metro line (Fontana stop, green line L3) or either Gran de Gràcia street or Via Augusta street -this way it's very easy and fast to go to/from downtown.
Check out www.bookings.com, do filter by District (Gràcia)... I just tried out and there are plenty of options. Something else is whether there'll be availability... September is a complicated month: weather is nicer than summer (not as hot!), there are plenty of congresses in the city, Catalonia's National Day is celebrated on Sep 11th, there are several major festivals (ie. La Mercè towards the end of the month), etc.
Actually, for those curious... Gràcia was established in 1626 when a convent was built there: Nostra Senyora de Gràcia (Our Lady of Grace). Gràcia was an independent municipality until it was annexed to Barcelona in 1897 along with other villages in the plain of Barcelona. The expansion of the Eixample district in the 19th century eventually led to the northward expansion of Barcelona, connecting Gràcia to the growing metropolis. Be warned that Gràcia is not monumental, nor has major landmarks (with a couple of exceptions: ie. Casa Vicens http://infocatalonia.eu/w/HKwcQ), nor wide streets or parks or anything that one would consider distinct. Don't expect a wow factor. Its uniqueness is based in the ambience of 'small town' within a city, the sense that's a patch of the city where life goes at a slower pace, where one could even say that's a glimpse on how Barcelona was 100 years ago. Gràcia must be visited in the afternoon, 6ish onwards, to appreciate this, if I may, simpler life so characteristic of smaller towns. For me, aside the main tree-lined squares, the epitome of what Gràcia is all about are Carrer Astúries, off Fontana Metro station (green line L3) and Carrer Verdi. Both are fairly short pedestrianised streets, like all streets in Gràcia (short that is!) with small shops, cafes, grocery stores and lots of people going about their business, strolling, meeting friends... but even the lively strip of bars on Carrer Verdi give little clue to the week-long revelry that attracts an estimated 1.5 million party-goers in August every year (http://infocatalonia.eu/w/FZHgQ)
L'Eixample, on the other hand, is a district between the old city (Ciutat Vella) and what were once surrounding small towns (Sants, Gràcia, Sant Andreu etc.), constructed in the 19th and early 20th centuries. My grandmother she lived in Gràcia and used to say "let's go to Barcelona" when referring to what's today downtown. And she recalled her mum mentioning that there were 'fields' between Gràcia and Barcelona before the city expanded north towards the independent village of Gràcia in what's today l'Eixample -which btw, means "widening" in Catalan. Some curiosities: http://www.paseodegracia.com/en/historia/a-trip-through-time/