Dinner in the centre:
We recommend eating dinner in the centre. The reason: restaurants in the Jewish Quarter are either very expensive or very touristic. In the centre you'll find more authentic alternatives. You shouldn't leave Córdoba without having tried "salmorejo" (like gazpacho but thicker), "rabo de toro" (bull's tail, meat stew made with this part of the bull), "pisto" (ratatouille) and "flamenquines" (veal with breaded ham).
If you're in the mood for dining outdoors, our recommendation is Casa Pisto (Taberna San Miguel), on Plaza San Miguel 1. The outdoor seating here is very nice and they offer all the mentioned typical dishes but the "flamenquines". Always order half portions (it'll be plenty). Dinner will run you around 30€ per person.
A cheaper and possibly better alternative is Taberna Salinas (Calle Tundidores 3), near Plaza Corredera. There is no outdoor seating but the restaurant has a lot of character. You can try all the typical dishes of Cordoba for around 6-7€ per plate. The croquettes are also very good (get the mixed ones). 3-4 dishes will be more than enough for 2 two people, and dinner should run you around 20€ per person.
After dinner we recommend going for a drink at Sojo Café, on the corner of Paseo de la Rivera and Calle San Fernando. Mixed drinks are 7€. In addition to the cosy Moorish decor, the views of the river are spectacular (you'll have to take an elevator up to the bar).
The city is very famous for the Festival de la Guitarra de Córdoba, which usually takes place in July. Check the website for any concert you might want to see.