In the first one, I would not build a campus where you have the IZ marker. You will have to wait ages to claim it or spend early gold buying it. That tile might also be a good campus location for a second or third city. I would put the campus on the wooded hill due east. That has an instant 3 science and 4 (same as the other location) if you place another district beside it. I am very content with 3 adjacency, which gives 50% more science if you run the rationalism policy. High adjacency is nice early, (though there is an argument that you don't want to go through the tech/civic trees too fast and raise district costs), but +1 science (or gold etc) is not very significant in the later game. The problem with that wooded hill location is that it robs your capital of a 2F 2P location, so I wouldn't be too keen to build the campus there too early, until I'd improved or bought some other tiles.
Before placing it, chop the woods down, and you could put the resulting production towards building the pyramids on the desert tile. That's an excellent tile for early pyramids. The grassland tile 2 east of the capital is not going to be of any use, so that's a good spot for an encampment or entertainment complex. If the latter, you could build the colosseum on the tile east of the desert copper and a theatre square on the desert copper, which would place the theater sq between the pyramids and colosseum and so generate 4 culture. That would also complete a triangle of 3 districts giving each an adjacency bonus. I'd put a CH on any plains square next to the river and be content with 2G making sure it does not hamper building the farms I need. (That city has no squares with surplus food, so I would be keen to build a water mill, and at least a triangle of farms centred on the wheat so I can work those plains hills. Or have another pan using trade rotes or wonders/buildings to get enough food to work the hills and grow the city to at least 10).
For map 2, you do realise that the city centre is a district, so your planned IZ and CH will get a district adjacency bonus, without needing the theater square? Ideally I wouldn't put a district on that theater sq tile as it could potentially have a number of uses. If Auckland claims the wheat tile nearest to it, then you need the theater square tile to form a triangle of farms with the remaining wheat. Or you could build the Ruhr wonder on it (which is going to be good in a city with so many hills) or the Big Ben wonder. The theatre square could then go on the plains tile west of the silk for a 2 culture adjacency. You might also be able to build a dam on that tile and boost the IZ by +2P, but probably not as I think only 1 edge of that tile is river. The campus is in an almost perfect location. Placed on a virtually useless desert tile, with +5 science!
Although some districts don't benefit from adjacency themselves (dams, encampments, entertainment complexes), they can be useful in bestowing adjacency bonuses on others. If you had settled on the geothermal fissure, then I would have been very tempted to build an encampment on the copper hill next to the campus, adding +1 to the campus adjacency and claiming a good defensive spot. However, I might not do so, because I would be losing a hill and maybe it would be better near Auckland. I hope this gives an indication of some of the factors I consider.
