One of the best day trips you can take from Coimbra is to the Mata Nacional do Buçaco (or National Forest of Buçaco) near the town of Luso. Not only is it free to enter, but it's incredibly beautiful and relaxing. If you want to explore the forest for longer than a day, you can always stay the night in the posh, but pricey Bussaco Palace Hotel, shown below. Apparently there's some sort of amazing 8 course dinner you can take part in at the hotel's restaurant, though I've never tried it.
For travelers who'd like to get there and back again without having to rent a car, there is a bus. The schedule is NOT easy to find, so be sure to bookmark it for your future trips. "Período de Aulas" and "Período Fora de Aulas" means "Period of Classes" (School season) and "Period Out of Classes" (School holidays during the summer and possibly winter), although from Coimbra to Buçaco and back, the schedules appear to be the same regardless of whether class is in session. "Dias Úteis" means weekdays and "Só aos Sábados" is "Only on Saturdays". The last bus for Coimbra leaves earlier than most from behind the palace at 18:27 (6:27 PM). Don't worry if it's not there on the dot - ours didn't arrive until half and hour later.
One thing we were confused about was where to catch the bus in Coimbra. Some buses leave from the Rodoviario (bus station) on Avenida Fernão de Magalhães and others leave from Portagem, while some stop at both. This bus originates from the Rodoviario, so that's where we caught it. It's kind of difficult to tell which bus is which there because some of them aren't marked. Also, there isn't a screen in the station displaying which buses are in which terminals or where they'll be stopping unlike most other bus stations. If all else fails, you can approach each driver and ask, "Vai Buçaco?" or "Going to Buçaco?" and they'll tell you.
Like every other bus journey, there are way more stops than the ones that are listed, and local residents will get out along the way. Another thing about most buses I've been on in Portugal is that they don't announce their stops like most drivers in the US do. In many places, you may have to ask the driver to let you know when your stop comes up or be super alert and check signs. I've definitely gotten off at the wrong stop before, or stayed on after my stop, not realizing. It takes some getting used to.
Buçaco is amazing. It's got a long history of being a sanctuary and preserve for nature and wildlife and contains over 700 species of plants. Back in the 1600's, some Carmelite monks began filling the forest with local and exotic trees, ferns and other plants and by 1643, Pope Urban VIII declared that anyone caught damaging the trees in Buçaco would be excommunicated. Despite a battle taking place here between the Duke of Wellington and Napoleon, the forest is looking no worse for wear about 200 years later.
There are miles (or should I say kilometers?) of trails going through lush scenery, past tropical plants and beautiful blooms. Buçaco has several ponds and pools and small streams crisscrossing through the park and little wooden bridges to cross them. There's a huge stone staircase as well with waterfalls running into pools down the center. Tables for picnicking were available, but if you didn't bring anything to eat and were feeling hungry, there is a cafe outside of the gift shop.
Buçaco makes a very pleasant journey if you're looking to get out of the city for awhile, plus it's accessible by public transport! Since I don't tend to rent cars when I travel, sometimes the outdoorsy or rural activities are beyond my access, but this is one of those places you can visit even if you don't have a car. Enjoy!