When taken from the Jewish perspective, it seems like the summer is a drag - fasts, the three weeks, all the tragedies in our history that occurred during this time. Is there anything positive one can say about the summer?
There is, first of all, an idea (though I can't recall the source) that Hashem intended to give us a holiday each month during the summer. (During the spring, we have Pesach in Nissan, Pesach Sheni in Iyar, and Shavuos in Sivan.) Due to the sin of the Golden Calf, we lost that privilege; but instead Hashem moved all of those holidays to Tishrei (which is why it's got four Yamim Tovim - its own plus the "missing" ones for the previous three months).
This would mean, then, that Tammuz contains something of the potential of Rosh Hashanah, Av of Yom Kippur, etc.
The month of Tammuz, specifically, contains the dates (the 3rd, 12th, and 13th) when the previous Lubavitcher Rebbe, R' Yosef Yitzchak Schneersohn, was saved first from a death sentence and then from exile, and was thereby enabled to continue his work of disseminating Judaism in the Soviet Union (and eventually in America, after his arrival here in 1940). R' Yosef Yitzchak's successor, R' Menachem Mendel, dubbed this month חודש הגאולה - the month of redemption - and often explained how these events and their aftereffects permeate the entire month (even the less-cheerful part from 17 Tammuz onward).
Jake mentioned Tu B'Av in a comment, and indeed there are also talks where the Rebbe explains why indeed that is one of the most joyful days on the Jewish calendar (as per Taanis 30b-31a): it represents the powerful rebound that comes after (and from) the deep descent of Tisha B'Av.
On a more "down-to-earth" level, summertime is when people tend to take it easier with school and work. In another of his talks, the Rebbe points out that this provides more time to strengthen one's Torah learning while also enjoying a vacation to relax and strengthen the body; in particular, for children, Jewish sleepaway camps are in a sense better than school, in that the child is immersed in a Jewish environment 24/7. (He once expressed the role of Camp Gan Israel, in particular, as א קאוואדלע וואו מ'קאוועט אויס חסידים - an anvil where chassidim are shaped.)
From here (emphasis added):
It is explained in Chasidut that our ongoing process of self-refinement is more dependent on our own initiative during the "male" half of the year, i.e. from Tishrei to Adar. During the "female" half of the year, i.e. from Nisan to Elul, G-d takes the initiative and our job is just to capitalize and respond to this initiative. The clearest indication of this is the festival of Pesach, in which we were pulled out of Egypt by G-d Himself. Similarly, the springtime renewal of nature, which occurs in Nisan, practically forces us to undergo a similar renewal of inspiration, and all we have to do is respond to it and ride the wave of renewal.
In Likutei Sichos 19 (page 160 footnote 21), The Lubavitcher Rebbe mentions this idea and points out the Likutei Torah Ha'Arizal parshat Vayeitzei. I didn't look it up, so I don't know what it says.
The Midrash (Shir Hashirim Rabba 7:4) Tells us (in the name of R' Yehoshua ben Levi) that just like there are 50 days between Pesach and Atzeret (Shavuot), there should also be 50 days between Sukkot and it's Atzeret (Shmini Atzeret). It gives a parable to explain why this is not the case:
A king had many married daughters, some lived close by, and some lived far away. One day they all came to visit their father, the king. The king told them, those of you that live close by have the time to go home and come back without too much hassle. Those that live far away however, do not have the time to go home and come back to visit. Therefore now that you're here, let us all take the opportunity and make a holiday.
So too, the Midrash continues, Shavuot, which is the Atzeret of Pesach, happens when the winter turns to summer, so we have time to go home and come back (and therefore Shavuot is 50 days after Pesach). Sukkot, on the other hand happens when summer is turning to winter. The conditions of the roads in the winter make it very difficult to travel, and it is not possible to go and come back 50 days later. Therefore, G-d says to make Shmini Atzeret right after Sukkot (instead of waiting 50 days).
That's the Midrash.
Chabad Chassidus points out that from the parable brought in the Midrash we see that the summertime is referred to as "close" ('those of you that live close by have the time to go home and come back without too much hassle') and the wintertime as referred to as "far".
Chabad Chassidus uses this to explain that service of G-d is closer to us and easier for us in the summer. The summer is a time when the sun is shining (hotter, longer days), and the sun is associated with a high level of G-dly revelation. Service of G-d in the wintertime, by contrast is farther away from us, and more difficult. -- (See paragraph 8 and the sources brought in the footnotes).
Shabbos Nachamu? (and a few char more)
Recall that the Hebrew calendar, along with all the Chagim, originates from the agricultural reality in Israel at ancient times. Summer was always pretty dull in terms of weather and resulting agricultural activity over here.
It also seems that summer is the best time to wage war or try to capture a city like Jerusalem. Steady weather, ability to leverage drought when laying siege to a city, and so forth. Thus the summer is thin with Jewish Holidays, and thick with the "negative" days - fasts, 3 weeks and so on.
This would be a consequence of terrain, weather and history - and not to imply any underlying Jewish outlook on the quality of each month or season
Of course summer was intended to be sad. Just that a bunch of tragedies happened; Temple times didn't have the misery we know associate with parts of the summertime.
For many people it's an opportunity to recharge their batteries, which can be a very important, healthy, appropriate thing.
Thinking in terms of everyday Biblical life, it would have been the time of:
And threshing [season] will overtake grape-harvesting [season], and grape-harvesting will overtake planting ...
Keeping busy was viewed as a blessing!