Reilu viikko sitten juhannuksena kävin Porvoossa.

"Vietin juhannuksen Porvoossa" = I spent the whole midsummer's eve in Porvoo
"Kävin juhannuksena" = I visited Porvoo during the midsummer's eve

Yksi minun työkavereistani oli suositellut minua näkemään sitä kaupunkille Porvoon vierailua.

"Näkemään kaupunkia" feels a bit unnatural here. I would rather say "to visit Porvoo" to include all sensations, not only sight.

Could also be just "suositellut minulle Porvoota" to make it even more compact.

Hän sanoi, että se, mikä erottaa Porvoon muista suomalaisista kaupungeista, on hyvin säiliynyt vanha kaupunki.

It's correct, but just a little bit cumbersome.

I would probably say: "Hän sanoi, että Porvoon erottava tekijä on hyvin säilynyt vanha kaupunki."
It is clear from the context that we are comparing to other Finnish cities here.

Juuri tämä kiinnosti minua, koska kaikissa suomalaisissa kapungeissa, joissa olin kävynyt, arkkitehtuuri oli aika modernia.

Lähdin Helsingistä bussilla Kampissa sijaitsevalta asemalta.

Correct, but could also just be "Kampin (bussi)asemalta" to be more compact.

Kävelin eteläänpäin ja heti huomasin heti kiinnostavia puutaloja.

The original is not incorrect, the word order here is somewhat flexible.

The original puts *heavy* emphasis on the 'right away' aspect, and very strongly conveys the expectation and desire of seeing wooden houses.

This tuned version puts the focus on the writer and their observation rather than the 'right away, immediately' aspect.

Ajattelin, että sellaisia taloja puuttuu muista kaupungeista, joissa olin nähkäynyt,; vaikka Espoosta, Helsingistä tai Tampereelta.

Ei ihme, koska moni lähti varmaan lähti viettämään juhannusta kesämökeilläeen.

Very natural use of "ei ihme"! This type of "wondering aloud" really adds to the natural feeling of the text.

The word "lähti" implies going somewhere to do something. "Oli kesämökeillä" versus "lähti kesämökeille".

Since most people also own their summer cottages I added the possessive suffix. If you want to emphasize the option of going to someone else's summer cottage, it should be left out.

Museotkin olivat kiinni, m. Menin ohi Runebergin kodin ohi, jossa hän asui aikanaan ja nyt sielläasui ja jossa nyt sijaitsee museo, mutta sekin oli kiinni.

Some word order fixes. "Jossa" needs to be repeated for the subclause.

It was already stated that museums were closed, so if we later want to highlight that a certain museum was *also* closed, we need to say that with '-kin': "Even that was closed."

Menin joen toiselle puolelle, josta löytyyi modernimpia rakennuksia.

I suppose it's not grammatically incorrect, but it felt a bit weird to change the tense from past to present midsentence.

Since this is a travel story, it feels good to highlight that on this particular day you found those more modern structures, rather than stating a general fact that there are some over there even to this day.

Yksi tutukuuluisimmista siellä sijaitsevista rakennuksista on Taidetehdas, joka on Porvoon kulttuuri- ja kongressikeskus.

"Tutuimmista" implies a very strong personal connection to the building, which doesn't seem to be the case -- if it was, I'd expect the writer to explain their bond to the structure.

Tuttu = familiar to me personally
Kuuluisa = popular, famous in general

Moni ravintoloista oli kiinni, mutta onneksi pari oli auki.

I thought it would be more natural to highlight that out of the all restaurants, many were closed but luckily a few were open.

The original is not grammatically incorrect, but it feels slightly weird to directly contradict what was said earlier in the later clause.

Löysin jonkierään kiinalaisen ravintolan ja päätin syödä lounaan siinä.

"Jonkin" feels a bit dismissive here, especially in written Finnish.

Se on ehdottomasti Porvoon mielenkiintoisin osa.

There is nothing grammatically wrong here, but the tense switches quite abruptly, almost as if you're ready to end the story here and jump to the conclusions. In the present tense this is a very strong general statement.

If it was past tense it would perhaps flow better as part of the developing story.

Tykkäsin erityisesti kapeista kaduista joidenkin talojen välillaä.

Sellaisia ei tosiaan ei löydy Suomen muista kaungeista.

Menin myös Isoon Linnamäkeen, josta on upeita näkymaisemiäa Porvoon yli.

Tense switch here as well. I would possibly rephrase into "jossa katselin upeita maisemia Porvoo yli" to weave it as part of the past tense story being told.