Belfast is a compact, low rise city surrounded by hills which you can be seen from many of the main streets. The City Hall provides the centrepiece with exceptional period architecture in surrounding buildings. The small size means that most places of interest are easily walked to and others a short bus ride away. A great way around the city is by public transport, a day rover ticket costs around £3.75p and is valid for unlimited rides after 9:30am.
Alternatively, there are plenty of taxi's around during the day and night but ask the fare first, some have fixed charges while others work on a meter, in rush hour the latter can cost a lot more than you might anticipate. Public transport moves much quicker in rush hour with special bus lanes.
You can also find sightseeing tours and guided walks, several can be found at Great Victoria Street, Royal Avenue and High Street. These are run by independent operators so shop around, you will certainly be approached at some stage by one of the ticket hawkers offering you a tour. You can also take a boat tour from a jetty near the Big Fish sculpture.
Walking around the city is very pleasant, the fabulous architecture reflects the grandeur and affluence that the city was built upon and there really are some classical pieces to see. Locations like the Cathedral Quarter with its network of small streets and venues makes exploring the city an interesting experience. I like the size of Belfast, it makes everywhere an easy, enjoyable walk plus a twenty minutes bus or car ride you can be on top of the Black mountain or Cave Hill enjoying a spectacular view over the city and some awesome walks. You can walk from City Hall to the Odyssey and Titanic Quarter, the heritage is well documented on information panels along the way.
If you like exploring then you will eventually come across the characteristic murals and neighbourhood markings which relate to the two main traditions, one side marks in red, white and blue, the other in green, white and orange. In some parts of the city these have become a tourist attraction. There are though small enclaves which are very strong in their particular identity, and although we have a long established peace agreement, to avoid any possible issues while your here I would recommend a neutral approach clothing and in particular the national identities of Britain, Ulster and Ireland. Especially try to avoid football/ hurling tops as these can be problematic if you go in the wrong area.
Having said that Belfast is a very friendly and welcoming city with an amazing amount of things to see and do while your here. As I mentioned earlier public transport offers a great way to see the city for a very reasonable charge. City Hall is where most buses stop and start from. Great Victoria Railway and Bus Station is a five minute walk away.