In this chapter, Solomon builds many other cities and infrastructure throughout Israel.
To begin, as with so many other parts of 2 Chronicles, this chapter also has strong parallels in the text of 1 Kings. For this chapter, it is a parallel text to 1 Kings 9:10-28. There are a few differences but the majority of the text is similar and it has the same general structure. This chapter has two main sections: Solomon's continued construction activities (v. 1-11), Solomon's religious devotion (v. 12-16). Verses 17-18 tell one other brief story about Solomon's partnership with Hiram in long distance trade.
I see the first section (Solomon's construction projects) as being a natural extension of the temple project. Basically, Solomon is a strong and wealthy ruler and Israel as a nation is quite successful as well. As part of that, we see in v. 7-8 that Solomon is conscripting vast numbers of non-Israelites for his building projects. Of course, we knew that from when he built the temple (2 Chronicles 2:17-18), but the point is that when you have 150,000 conscripted workers, you don't have them just make the temple and them stop. You have them keep building you stuff because why not? All of the infrastructure, organization and planning that went into making the temple can be easily redirected to other construction projects when the temple is finished, and that is exactly what Solomon does. Ignoring the religious justification, all of these building projects enhance Solomon's prestige and have military and economic benefits as well (the temple doesn't but these other projects do). It's only natural that he would keep building. The general picture we can take away from this is that Solomon is a very successful and powerful ruler. He has all of the trappings of a strong king including monumental construction projects and lots of slave labor. This is one of the high points in Israel's political history.
The second section (Solomon's religious devotion) is a response to God's promise in the previous chapter. In 2 Chronicles 7:17-18, God says that he would establish Solomon's kingdom if Solomon walks faithfully in the same way as his father David. What I take away from this chapter is that the Chronicler is saying yes, Solomon did walk in his fathers ways and was an honorable and devoted king. 1 Kings 11 certainly gives us a different picture of Solomon, claiming that he married foreign women who "turned his heart away after other gods" (1 Kings 11:4). 1 Kings 9 does record Solomon going to make offerings at the temple three times a year, but it does not include the additional details that we see in verses 13-16. Verse 13 establishes Solomon's faithfulness towards the commands of Moses, and verses 14-15 establish Solomon's faithfulness towards the commands of David. If we view Moses as being the architect of the tabernacle and David as the architect of the temple, then Solomon is a person who is faithful to both the old and the new patterns.
Out of these two sections, we can draw several patterns.
The first is idealization of Solomon as a ruler. This is something I've touched on multiple times when going through Chronicles, which is that Chronicles has a general tendency towards omitting the stories that make David or Solomon look bad and including extra details that tend to make them look good. In this chapter, it shows up by the emphasis on Solomon's religious devotion that is notably more detailed than the parallel description in Kings, and by omitting the record of Solomon's later idolatry.
The second is the continuation of the temple building project. This chapter is a transition between the temple narrative to the royal succession narrative, and it does that by describing the remainder of Solomon's life before moving on to the next generation. It specifically describes his building projects which are related to the temple project for the reasons I described above. We also see the temple project continuing in Solomon's faithful devotion to the annual sacrifices and his adherence to David's division of the priests and Levites. Basically what this shows is that after the temple was completed, Solomon continued to perpetuate the religious rituals that were mandated at the temple by both Moses and David. Solomon's faithfulness in the perpetual rituals is a natural extension of Solomon's faithfulness in building the temple in the first place.
The third pattern is Solomon's response to God's command. We see Solomon faithfully obeying in David's footsteps, thereby ensuring that he would have a everlasting kingdom in accordance with God's promise. In the language of Kings and Chronicles, "walking in the ways of his father David" is a kind of benchmark for whether a certain king was good or bad. Those who follow the ways of David are "established" (2 Chron 7:18) and those who don't are cast out or punished or whatever is the opposite of being "established". I mentioned that this "walking in the ways of your father David" is going to be one of the major themes of Chronicles, and as it relates to king Solomon, the Chronicler wants to make it clear that Solomon obeyed the LORD in the same way as his father, and that Solomon was a godly ruler. The book of Kings is a bit more circumspect on Solomon's reign, but also has a largely-positive outlook on Solomon as a ruler.
In the next chapter, Solomon's life story concludes with his encounter with the queen of Sheba.