One of my favourite cities, few quick tidbits below (stuff to see, do). Overall it is a pretty easy city to navigate and no need for any sort of special care/caution other than the obligatory "keep your wallet all the way down your pocket/bag and don't leave your stuff" like in every other big city.
Great mixture of culture and easy access to everyday stuff. There's a great restaurant, bar/pub or sth like this every 10 yards
Visit "Chimera Brewpub", which despite it's english name offers great portuguese craft beer.
- Get either a Metro/Bus pass or the "Lisboa card" which costs about 13-16 € a day and gives unlimited travel and free entry for pretty much everything. Should be available at pretty much every hotel as well as tourist info.
- there's still a regular historic tram and a few funiculars to use, pretty neat. There's also newer ones catering for tourists
- the castelo overlooking the town is well worth a visit and the way there is very atmospheric going through one of the oldest neighbourhoods.
- Belem is a must-do, lots of historic monuments in a small area.
- Depending on how much time you have, you could do a day trip to Sintra/Cascais. Both can usually be booked in one tour, Sintra has amazing palaces, views and scenery while Cascais has great beaches to wander around. Both only 45 minutes with public transport if you want to do it independently.