Taking as a starting point Campo Pequeno, in the center of the city and with very good connections to all public transports as well as Lisbon sightseeing (red line) and yellow-bus (Olisipo tour), which has a stopping point here.
Take a look at the building outside and inside. If you have quite some time in Lisbon and want to visit the inside of the bullring wait until 10 o'clock, because that is when they open their doors. Enter any of its side doors, that usually are ajar, and go around the benches. You can see its interior, although less beautiful than the outside, in my opinion.
I suggest you to take the bus 727 in Campo Pequeno (Avenida da Republica). This bus has a frequency between 11 to 15 minutes, but give it time because it has a very long route and goes by routes with heavy traffic, so take your time and enjoy to observe the city. I think it pays off because its trajectory offers an excellent overview of the city.
Pass the Largo do Rato and follow the street of São Bento, interesting for its concentrated antique shops. Reach the palace of São Bento, where the Parliament is located.
I highly recommend the guided visit to the palace and the Parliament. It is an extraordinary building!
The bus route then meets the Tejo river, in Santos, and runs along the street of Janelas Verdes, with interesting palaces, mostly not visited, except in particular periods, to the Old Arts Museum. It is not to miss!
I recommend the visit between Wednesday and Friday. The museum opens at 10 am. This museum will take time to visit (recommend taking 2-3 hours), trust me, it is not wasted time.
The Old Arts Museum has a very rich collection!
You can take advantage of it, if it is lunchtime when you are there, do have lunch in the museum's restaurant, which has an excellent terrace in the garden, or, in Le Chat, which has a terrace with a magnificent and unforgettable view over the Tejo river.
The route of 727 goes on to Belém, and if you have not spent half the afternoon already delighting yourself with the museum and the view, you will still have time to continue on its route to Belém.
Here, in a few square meters, there are at least 6 unforgettable and also impossible places to visit in a single afternoon.
You will have to choose what to do first and also, depending on the time you have to visit Lisbon, eventually take another day for the rest, combining with a not less fantastic, riverside walk...
Those are the Belém Tower, the Discoveries Monument (Padrão dos Descobrimentos), the Jerónimos Monastery, the Tropical Botanical Garden, the CCB Museum of the Berardo Collection (Contemporanean Art), Old Carriages Museum, the Pastels of Belém Factory and Store...and many others, depending on your interests
I do not like when other people tell me what to do on my trips, so I'm not going to do it to you either.
This is just a visiting suggestion that takes advantage of the 727 bus line for a first great view of the most western part of the city.
Hence the so-called line of Cascais, to be seen at another time.
As for Belém, for the vastness of highlights that the place concentrates, it is also worthy of an exclusive post.