Well, HarrisLyon is/are certainly location experts, but I'm not sure I can agree on this...or with you!
First, don't count on temperature staying in the 70s...could change. And don't dismiss L'Eixample as "touristy"--it's a very large and varied area of the city from quite far west to quite far east. If anything, many areas of it are far less touristy than a good part of Gracia.
On the other hand, the two apartments you're looking at are not all that far away; we usually stay further out, near Sant Pau hospital. If you don't feel like walking into the Ciutat Vella for dinner in the evening...well, there are plenty of people finding their way to Gracia for dinner every night!
That said, the second apartment has a longish walk to either Joanic or Verdaguer staations on the Metro, while the second is quite near Fontana. Of course, if the first is more appealing to you, check out the bus options as well.