If you are interested in...
If you are interested in astronomy, you would want to visit the observator on the Calar Alto. Please don't go there during the night (see my nightlife entry). I've seen many people around the telescoped during the day, maybe because the sight to the surrounding mountains is kind of cool. Don't expect an astronomer or staff member to show you around in the telescope buildings. During the day, the astronomers try to sleep and the staff keeps the telescopes in good shape.
Plaza e Iglesia de San Pedro
This is a favourite spot in the old quarter, specially during the Cruces de Mayo celebrations, when open air stands with music, food and drinks are open all over the place. The church was built in 1800 over the ruines of the San Francisco monastery from 16th century and its style is neoclassic.
Historic City of Almeria
Almeria is a fairly modern city and port in the east of Andalucia. The city is dominated by the Alcazaba, built in the 11th century when Almeria was an independent kingdom, and one of the most commercially active and weathiest districts in Spain. The citadel once housed a palace, immence gardens and some 20,000 people. Once it was reputed to rival Granada in grandeur, but time has taken its toll on the Alcazada, the last of the stuccowork was supposedly sold off by locals in the 18th. century. From the Alcazaba's hilltop location, good views of the coast are visible.
Another point of interest is the cities fortified cathedral, which was built in the 16th century when this coast was plagued by Turkish and Barbary pirates. Its corner towers once housed cannons for the defence of the populace that ran here for security during the raids.
Twenty kilometers north of Almeria, you will find Los Millares, a 4000 year old settlement, protected by strong walls.