1. TRANSPORT

2. MEANS OF TRANSPORT
First of all, remember that “transport” is an UNCOUNTABLE NOUN. So you cannot say “a transport”. The most natural collocation is a MEANS of transport. Means is singular and plural. Other possibilities: forms of transport, ways of transport.

3. TO GET AROUND This is the verb you need to express “para moverse”
The tram is the quickest means of transport to get around (the city)

4. SUPERLATIVES (LITERAL TRANSLATIONS)
In Spanish, we can very well say “este medio de transporte es el más rápido”. However, in English leaving a superlative on its own doesn’t sound natural at all (This means of transport is the fastest*). So, why don’t you use an alternative like this: This is the fastest means of transport (superlative + noun)

5. “TURÍSTICO”
“Touristic” is not native English, believe me. I don’t think a native speaker would ever use that word. If you hear it, it’s very likely to be uttered by a non-native speaker. So, what can I say to mean “turístico”? Here you have several examples:
It’s a TOURIST place/city/office.
Benidorm is quite a TOURISTY city (negative)

6. “SITIOS TURÍSTICOS” Places of interest. Tourist sites.
Major tourist attractions.
We saw the sights.
We went sightseeing.
“Touristic places*”… Nope! ;)

7. “CONOCER” CIUDADES, CULTURAS…
You MEET people, that’s clear.
For cities, cultures and so on, use GET TO KNOW. It involves a process, so we don’t say I like knowing cultures/countries, but “getting to know”. You can also use VISIT, obviously.

8. FURTHER COMMENTS CONNECT TO (not “with”)
“hacer transbordo”: change (trains, buses, lines…). You can change to line three at this station. You can change trains at Paddington station.
Structures you need to use: COMPARATIVES, SUPERLATIVES, specific vocabulary (TRAVEL CARD, GET AROUND, TRAFFIC JAM, RUSH HOUR…)
Useful adjectives: PACKED, CROWDED (both of them mean “lleno de gente, abarrotado”).