There actually are a range of plants that do well in brackish water, including several species that naturally occur in brackish water habitats. The problem is that these species tend to prefer low end salinities, up to about 25% seawater, or SG 1.005 at 25 C. The only widely traded mid to high salinity species is
Samolus valerandi, which will take almost full strength seawater. However, it's a difficult species to grow, requiring a good substrate and strong lighting.
Sea and turtle grasses are available, and these will do well at mid to high salinities, depending on the species. The same goes for mangroves, though I don't personally rate mangroves very highly given their size: they are, after all, trees, so at best short-term additions to a home aquarium.
Caulerpa species are not particularly tolerant of brackish water, and even the hardiest species will not do well below 75% seawater salinity (less than SG 1.018 at 25 C). There are lots of truly euryhaline algae, some of which are very decorative, but you will need to collect these yourself. The exception here are moss balls,
Cladophora aegagropila, which are widely sold but only tolerate low levels of salinity (up to around SG 1.003, maybe a little higher).
Anyway, if you want to grow plants, take a look at my
Brackish FAQ for a run through the most widely traded species. Java fern for example generally does very well up to SG 1.005, though I will make the observation that I have never found this species particularly easy to grow, even in freshwater tanks. I tend to recommend people buy one well-established "mother plant" on a bogwood root, rather than trying to establish the species themselves from cuttings or potted plantlets. Another good species is
Cryptocoryne ciliata, a big, brackish water specialist widely available via mail order if not often seen in pet stores. The hardy hybrid Crypts are pretty good, too, though they will need to be kept at SG 1.003 or less. Often, the reason plants fail in brackish water isn't the salinity issue but the fact the rest of the system is inadequate: shallow, poor substrate; no fertilisation; lack of strong lighting; and perhaps even lack of CO2 (though most brackish water systems will use bicarbonate from the water instead).
The bottom line is this: if you want plants, keep your fish at a low salinity (25% seawater, or SG 1.005 at 25 C). This is perfectly adequate, if not perhaps ideal, for green spotted puffers. Assuming water quality is good and water chemistry is stable, they aren't going to have a shorter life because they're at SG 1.005 compared with SG 1.015 or 1.025.
On the other hand, if you want a mid to high salinity system, going to whole hog to SG 1.018 or more will allow you to keep seagrasses and
Caulerpa spp.
Cheers, Neale