The biggest (I think) recreational forest immediately next to Vaasa is the one at Pilvilampi (Finn. cloud pond), which can even be easily reached by foot from the Ristinummi residential area of Vaasa. Unlike for example Öjen at Sundom to the southwest, Pilvilampi is not a protected nature area, just a commercial forest (and there are quite a lot of clearings of various age in it).
There is a relatively dense network of forest roads and trails in the Pilvilampi woods, with several laavus (lean-to shelters), kota huts and one day hut on Storhälleberget Hill. In winter most of these turn into skiing tracks, and in fact the tracks, the laavus and the day hut are maintained by Vaasan Latu ry (Vaasa Ski Association). It is possible to hike or ski all the way from Vaasa to Skatila village, on the west bank of Kyrö River that forms the natural eastern border of the Pilvilampi woods.
The name Pilvilampi of course refers to an actual small lake in those woods. It is just a short distance from the parking lot on Vaasa side of the woods (on Kappelinmäentie Road, pretty much across the Uponor plant).
Now the curious thing about Pilvilampi is that it is in fact a completely artificial lake, and a part of Vaasa water supply. The city of Vaasa proper doesn’t have any rivers in it, just some small brooks (many of which are partially or completely underground now). It gets all its drinking water from the Kyrö River. Kyrö River (Kyrönjoki) is the most important river of South Ostrobothnia, over 180 km long, with vast fields on lakeus plains stretching along the entire length of its valley. It has more than enough water for Vaasa but it needs to be pumped through Pilvilampi woods first, which is about 7 km distance as the crow flies.
The actual water intake is located in the village Båskas. Vaasa Municipality at the moment only consists of the city proper (plus Sundom Village, the exclave of Vähäkyrö and a part of the archipelago) and Båskas is actually located in the rural municipality of Korsholm that surrounds Vaasa; however if you look at the topographical map, the small area of the water intake itself is specifically also designated as Vaasa territory. The pipes starting at Båskas go to the west through the woods, first reaching the small Kalliolampi (Finn. rock pond) pond, where the water is treated for the first time.
The much bigger Pilvilampi serves as intermediate water reserve for Vaasa. Its surface is 1.3 km2 large, and it can contain up to 3.3 million m3 of water, a two months water supply for the city. This comes useful during the spring floods (Ostrobothnian floods is a whole different interesting subject really), when the Kyrö waters get dirty enough it makes little sense to treat them. It is actually rather noticeable that the Pilvilampi level is not constant:
From Pilvilampi the water goes to the water treatment plant at the edge of Vaasa. It takes about two months for Kyrö water to travel all the way from the river to the water treatment plant.
At the water treatment plant the water gets thoroughly treated and disinfected in several stages. From there on it goes to households and industry, but there is one more intermediate point, the Vaasa water tower. The tower is actually a rather prominent landmark of the central Vaasa. It can hold only 500 m3 of water, but still serves to balance pressure in the water supply network. It is actually the oldest (1915) water tower in Finland still in use.
The tap water in Vaasa is perfectly clean, safe to drink and rather tasty (as is everywhere in Finland really).
Vaasa sewage gets treated at the Påtti plant in the northwest of the Palosaari area. Despite being very close to Vikinga, a rather luxurious detached house area in the north of Palosaari, it sometimes gives off pretty nasty smells when the wind is unfortunate. But the treated wastewater is clean enough that it can be dumped into the Varisselkä Bay (Finn. crow expanse) of the sea.
Both water supply and wasterwater treatment are managed by Vaasan Vesi Oy (Vaasa Water Company), which has a website with rather detailed explanations of the whole process (only in Finnish and Swedish but you can at least watch the introductory video on the page I linked, if I somehow made you extremely interested in Vaasa water supply). Vaasan Vesi Oy was established in 1915 (the water tower was constructed in this year; before 1915 water in Vaasa only came from wells), and the water supply through Pilvilampi dates from the 1930s, although it was of course continuously improved through the ages. Vaasan Vesi Oy is wholly owned by the Vaasa Municipality. It maintains 997 km of water pipes, 547 km of sewage pipes, and employs 59 people.
As of 1.1.2019, Vaasan Vesi Oy charges 1.45€ per m3 of tap water, and 2.17€ per m3 of sewage (prices include VAT). It is common to pay for your water consumption when you rent an apartment, but not universal (in my rental apartment from Pikipruukki, the municipal housing company, I do not pay far water separately). For owner-occupied dwellings you of course pay for what you actually consume.